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Mathematics

DU B.SC.(H) PHYSICS, SEM-IV: NUMERICAL ANALYSIS - RANJANA MEHTA

Author

RANJANA MEHTA

Cover Price : Rs 225.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127475
YOP : 2016

Binding : Paperback
Total Pages : 124
CD : No

About the Book :- This book is useful for various graduate and postgraduate courses in Mathematics, Physics, Computer Science. The book covers the syllabus for B.Sc(Hons.) Physics, IInd Year, Semester-IV for the paper-16,PHHT-414. This text has a student friendly approach with an easy to read writing style and a perfect blend of theory and numerical. It presents all the basic material in one place and gives an opportunity to understand the topic in the most easy and comfortable way. A large number of examples are used to explain the concepts. The book contains number of exercises to help build confidence in students. Contents :- 1. Errors and Iterative Methods 2. Solution of Algebraic Transcendental Equations 3. Matrices and Linear System of Equations 4. Interpolation 5. Least Square Approximation 6. Numerical Differentiation 7. General Quadrature Formula 8. Solution of Initial Value Problems References About the Author :- Dr. Ranjna Mehta is an Associate Professor in the Department of Mathematics at Sri Venkateswara College. She has over 36 years of teaching experience at the undergraduate level. Her area of interest are Numerical Analysis, Calculus, Geometry (two and three dimensional), Algebra, Functional Equations. She did her Ph.D entitled "Functional Equations on Algebraic Structures" from University of Delhi in 1982. Four of her research papers have been published in Indian and Foreign journals. She attended one science conference in Bombay in 1976. She attended various work-shops held in North and South Campus in the Department of Mathematics. Recently, She has published one book entitled "Numerical Methods and Programming" from Ane Books Pvt.Ltd.

Algebra : Fields and Galois Theory - Falko Lorenz

Author

Falko Lorenz

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 8181289803
YOP : 2008

Binding : Paperback
Total Pages : 304
CD : No

About the Book :- Algebra : Fields and Galois Theory The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader thorough interesting subject matter while assuming only the background provided by a first course in linear algebra. The book focuses of field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. This book contain numerous exercises and can be used as a textbook for advanced under-graduate students. From Reviews of the German version :- This is a charming textbook, introduction the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews Contents :- Foreword 1 Constructibility with Ruler and Compass 2 Algebraic Extensions 3 Simple Extensions 4 Fundamentals of Divisibility 5 Prime Factorization in Polynomial Rings. Gauss’s Theorem 6 Polynomial Splitting Fields 7 Separable Extensions 8 Galois Extensions 9 Finite Fields, Cyclic Groups and Roots of Unity 10 Group Actions 11 Applications of Galois Theory to Cyclotomic Fields 12 Further Steps into Galois Theory 13 Norm and Trace 14 Binomial Equations 15 Solvability of Equations 16 Integral Ring Extensions 17 The Transcendence of ð 18 Transcendental Field Extensions 19 Hilbert’s Nullstellensatz Appendix: Problems and Remarks Index of Notation Index.

Algebra - Volume I - B. L. van der Waerden

Author

B. L. van der Waerden

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181288868
YOP : 2008

Binding : Paperback
Total Pages : 272
CD : No

About the Book :- ...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century. - Saunders MacLane, Notices of the AMS How exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every would-be algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a first-rate (some would say, the best) source for the great range of material it contains. - David Eisenbud, Mathematical Sciences Research Institute Van der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today. - Robin Hartshorne, University of California, Berkeley Contents :- 1. Numbers and Sets; 2. Groups; 3. Rings and Fields; 4. Vector Spaces and Tensor Spaces; 5. Polynomials; 6. Theory of Fields; 7. Continuation of Group Theory; 8. The Galois Theory; 9. Ordering and Well Ordering of Sets; 10. Infinite Field Extensions; 11. Real Fields; Index.

 

Applied Numerical Analysis - Gerald

Author

Gerald

Cover Price : Rs 295.00

Imprint : PG / Addison Wesley
ISBN : 8178085674
YOP :
Edition :

Binding : Paperback
Total Pages : 0
CD : No

Mathematics / Management

ANE

Introduction to Linear Algebra, 2016 - Inder K. Rana

Author

Inder K. Rana

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789380156965
YOP : 2016

Binding : Paperback
Total Pages : 288
CD : No

About the Book There are two aspects of linear algebra: abstract and applied. Both these aspects play important role in diverse branches of mathematics, physics, engineering, economics, and so on. The aim of this book is to present both these aspects of linear algebra. We shall try to show how abstract concepts arise out of applications and physical needs, and how abstract concepts can be applied in various problems. Normally, students are taught matrices and determinants in the first introductory course in linear algebra. We shall assume familiarity with the concept of matrices only. However, we do give a brief introduction of matrices in chapter 2. We will relate the origin and use of these concepts in linear algebra. The book contains a moderate set of exercises. We intend to bring out an interactive e-version of the book in a CDROM. A preview of the same is available on the website www.math4all.in. Contents 1. From Geometry to Algebra-I: The Euclidean Space R3, 2. Systems of Linear Equations, 3. Linear Independence and Dependence of Vectors, 4. Determinants, 5. Vector Spaces, 6. Linear Transformations, 7. From Geometry to Algebra-II: Inner Product Spaces, 8. Orthogonal Projections and Orthogonal Basis, 9. Isometries and Orthogonal Matrices, 10. Diagonalization and the Spectral Theorem, 11. Applications of Diagonalization, Answers, Index About the Author Dr. Inder K. Rana is Professor at the Department of Mathematics, I.I.T. Bombay, with a teaching experience of more than 30 years. He was awarded the “C.L.C. Chandana award for the year 2000” for excellence in teaching and research in Mathematics, and also awarded the “Excellence in Teaching award for the year 2004” by I.I.T. Bombay. Other books authored by him include “An Introduction to Measure and Integration” published by American Mathematical Society, and “From Numbers to Analysis” published by World Scientific Press.

Experimental Number Theory - Fernando Rodriguez Villegas

Author

Fernando Rodriguez Villegas

Cover Price : Rs 595.00

Imprint : Oxford University Press
ISBN : 0199548729
YOP : 2008

Binding : Paperback
Total Pages : 232
CD : No

About the Book :- This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions. Sample programs are written in GP, the scripting language for the computational package PARI, and are available for download from the author's website. Contents :- Preface 1. Basic examples 2. Reciprocity 3. Positive definite binary quadratic forms 4. Sequences 5. Combinatorics 6. p-adic numbers 7. Polynomials 8. Remarks on selected exercises References Index. About the Author :- Fernando Rodriguez Villegas, Department of Mathematics, University of Texas at Austin.

Calculus 2nd ed, Reprint - J.P. Singh

Author

J.P. Singh

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127260
YOP : 2015

Binding : Paperback
Size : 5.50" X 8.50"
Total Pages : 688
CD : No

About the Book The second edition of this book is the result of the enthusiastic reception given to the earlier edition received from the students and teachers, who are the end users of this book. The book covers the complete syllabus of BCA semester-I of GGSIP University. It introduces calculus and its techniques at undergraduate level in a simplified manner. Salient features: -Text is self-explanatory and the language is vivid and lucid -Contains numerous examples that illustrate the basic as well as high level concepts of the concerned topics -Additional questions provided in all the chapters for practice -Most of the questions conform to the trend in which the questions appear in GGSIP University Contents 1. Matrices and Determinants 2. Eigen Values and Eigen Vectors 3. Limits 4. Continuous Functions 5. Differentiation 6. Successive Differentiation 7. General Mean Value Theorems 8. Indeterminate Forms and L' Hôpital Rule 9. Maxima and Minima 10. Asymptotes 11. Integration and its Techniques 12. Reduction Formulae 13. Beta and Gamma Functions, End Term Examination Papers, Some Useful Trigonometric Results/Identities About the Author J.P. Singh is a professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini (Affiliated to GGSIP University), Delhi. He has more than 14 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a certified Six Sigma Green Belt from Indian Statistical Institute, Delhi. He is a lifetime member of Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Stochastic Process, Discrete Mathematics, Mathematical Statistics, Numerical Methods, Number Theory and Theory of Computation.

Algebra - Volume II - B. L. van der Waerden

Author

B. L. van der Waerden

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181288875
YOP : 2008

Binding : Paperback
Total Pages : 296
CD : No

About the Book :- ...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century. - Saunders MacLane, Notices of the AMS How exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every would-be algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a first-rate (some would say, the best) source for the great range of material it contains. - David Eisenbud, Mathematical Sciences Research Institute Van der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today. - Robin Hartshorne, University of California, Berkeley Contents :- 12. Linear Algebra; 13. Algebras; 14. Representation Theory of Groups and Algebras; 15. General Ideal Theory of Commutative Rings; 16. Theory of Polynomial Ideas; 17. Integral Algebraic Elements; 18. Fields with Valuations; 19. Algebraic Functions of One Variable; 20. Topological Algebra; Index.

Short Calculus - Serge Lang

Author

Serge Lang

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181289742
YOP : 2008

Binding : Paperback
Total Pages : 272
CD : No

About the Book :- This is a reprint of A First Course in Calculus, which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students background was not as substantial as it might be. We are now back to those times, so it is time to start over again. There are no epsilon-deltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950. Contents :- Numbers and Functions * Graphs and Curves * The Derivative * Sine and Cosine * The Mean Value Theorem * Sketching Curves * Inverse Functions * Exponents and Logarithms * Integration * Properties of the Integral * Techniques of Integration * Some Substantial Exercises * Applications of Integration * Taylor's Formula * Series * Appendix 1. Epsilon and Delta * Appendix 2. Physics and Mathematics * Answers * Index.

Business Mathematics for BBA, 2014 - J.P. Singh

Author

J.P. Singh

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127826
YOP : 2014

Binding : Paperback
Total Pages : 640
CD : No

About the Book This book has been written for undergraduate students pursuing Business Mathematics as their subject. The book primarily aims at students preparing for BBA, Semester I examination conducted by GGSIP University. This book consists of twelve chapters. All the chapters have been supplied by numerous solved examples and exercises along with their answers. The main objective of this book is to provide useful self-study material for the students which will not only enhance students' understanding of the concept discussed but will also prepare them for examination. Salient features: 1. It covers the complete syllabus of BBA Semester I of GGSIPU. 2. The text material is self-explanatory and the language is vivid and lucid. It can be used for sophomore-level course in Business Mathematics. 3. More than 415 solved examples of different types and different levels have been included. 4. Most of the questions conform to trend questions appearing in GGSIPU. Contents 1. Permutation and Combinations 2. Mathematical Induction 3. Sequence and Series 4. Matrices and Determinants 5. Applications of Matrices to Business and Economics 6. Differentiation 7. Applications of Differentiation 8. Partial Differentiation and its Applications 9. Integrations 10. Applications of Integration in Business and Economics 11. Differential Equation and its Applications 12. Vectors About the Author J.P. Singh is a Professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini (Affiliated to GGSIP University), Delhi. He has more than 14 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi. He is a lifetime member of the Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Stochastic Process, Discrete Mathematics, Mathematical Statistics, Numerical Methods, Number Theory and Theory of Computation.

Classical Algebra - Roger Cooke

Author

Roger Cooke

Cover Price : Rs 2,995.00

Imprint : Wiley
ISBN : 9788126553624
YOP : 2015

Binding : Hardback
Total Pages : 218
CD : No

Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors. This book successfully ties together the disconnect between classical and modern algebra and provides readers with answers to many fascinating questions that typically go unexamined, including: What is algebra about? How did it arise? What uses does it have? How did it develop? What problems and issues have occurred in its history? How were these problems and issues resolved? The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven "lessons" that are intended to give the reader further insight on classical algebra, each chapter contains thought-provoking problems and stimulating questions, for which complete answers are provided in an appendix. Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics. Contents Preface Part 1. Numbers and Equations. Lesson 1. What Algebra Is. 1. Numbers in disguise. 1.1. Classical and modern algebra. 2. Arithmetic and algebra. 3. The environment of algebra: Number systems. 4. Important concepts and principles in this lesson. 5. Problems and questions. 6. Further reading. Lesson 2. Equations and Their Solutions. 1. Polynomial equations, coefficients, and roots. 1.1. Geometric interpretations. 2. The classification of equations. 2.1. Diophantine equations. 3. Numerical and formulaic approaches to equations. 3.1. The numerical approach. 3.2. The formulaic approach. 4. Important concepts and principles in this lesson. 5. Problems and questions. 6. Further reading. Lesson 3. Where Algebra Comes From. 1. An Egyptian problem. 2. A Mesopotamian problem. 3. A Chinese problem. 4. An Arabic problem. 5. A Japanese problem. 6. Problems and questions. 7. Further reading. Lesson 4. Why Algebra Is Important. 1. Example: An ideal pendulum. 2. Problems and questions. 3. Further reading. Lesson 5. Numerical Solution of Equations. 1. A simple but crude method. 2. Ancient Chinese methods of calculating. 2.1. A linear problem in three unknowns. 3. Systems of linear equations. 4. Polynomial equations. 4.1. Noninteger solutions. 5. The cubic equation. 6. Problems and questions. 7. Further reading. Part 2. The Formulaic Approach to Equations. Lesson 6. Combinatoric Solutions I: Quadratic Equations. 1. Why not set up tables of solutions?. 2. The quadratic formula. 3. Problems and questions. 4. Further reading. Lesson 7. Combinatoric Solutions II: Cubic Equations. 1. Reduction from four parameters to one. 2. Graphical solutions of cubic equations. 3. Efforts to find a cubic formula. 3.1. Cube roots of complex numbers. 4. Alternative forms of the cubic formula. 5. The \irreducible case. 5.1. Imaginary numbers. 6. Problems and questions. 7. Further reading. Part 3. Resolvents. Lesson 8. From Combinatorics to Resolvents. 1. Solution of the irreducible case using complex numbers. 2. The quartic equation. 3. Viµete's solution of the irreducible case of the cubic. 3.1. Comparison of the Viète and Cardano solutions. 4. The Tschirnhaus solution of the cubic equation. 5. Lagrange's reflections on the cubic equation. 5.1. The cubic formula in terms of the roots. 5.2. A test case: The quartic. 6. Problems and questions. 7. Further reading. Lesson 9. The Search for Resolvents. 1. Coefficients and roots. 2. A unified approach to equations of all degrees. 2.1. A resolvent for the cubic equation. 3. A resolvent for the general quartic equation. 4. The state of polynomial algebra in 1770. 4.1. Seeking a resolvent for the quintic. 5. Permutations enter algebra. 6. Permutations of the variables in a function. 6.1. Two-valued functions. 7. Problems and questions. 8. Further reading. Part 4. Abstract Algebra. Lesson 10. Existence and Constructibility of Roots. 1. Proof that the complex numbers are algebraically closed. 2. Solution by radicals: General considerations. 2.1. The quadratic formula. 2.2. The cubic formula. 2.3. Algebraic functions and algebraic formulas. 3. Abel's proof. 3.1. Taking the formula apart. 3.2. The last step in the proof. 3.3. The verdict on Abel's proof. 4. Problems and questions. 5. Further reading. Lesson 11. The Breakthrough: Galois Theory. 1. An example of a solving an equation by radicals. 2. Field automorphisms and permutations of roots. 2.1. Subgroups and cosets. 2.2. Normal subgroups and quotient groups. 2.3. Further analysis of the cubic equation. 2.4. Why the cubic formula must have the form it does. 2.5. Why the roots of unity are important. 2.6. The birth of Galois theory. 3. A sketch of Galois theory. 4. Solution by radicals. 4.1. Abel's theorem. 5. Some simple examples for practice. 6. The story of polynomial algebra: a recap. 7. Problems and questions. 8. Further reading. Epilogue: Modern Algebra. 1. Groups. 2. Rings. 2.1. Associative rings. 2.2. Lie rings. 2.3. Special classes of rings. 3. Division rings and fields. 4. Vector spaces and related structures. 4.1. Modules. 4.2. Algebras. 5. Conclusion. Appendix: Some Facts about Polynomials. Answers to the Problems and Questions. Subject Index. Name Index. Roger Cooke, PhD, is Emeritus Professor of Mathematics in the Department of Mathematics and Statistics at the University of Vermont. Dr. Cooke has over forty years of academic experience, and his areas of research interest include the history of mathematics, almost-periodic functions, uniqueness of trigonometric series representations, and Fourier analysis. He is also the author of The History of Mathematics: A Brief Course, Second Edition (Wiley).

ADVANCES IN PDE MODELING AND COMPUTATION - S. SUNDAR

Author

S. SUNDAR

Cover Price : Rs 1,195.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789383656042
YOP : 2014

Binding : Hardback
Total Pages : 324
CD : No

About the Book This book on "Advances in PDE Modeling and Computation" is a collection of invited articles from active established researchers who are working in the area of PDE modeling and PDE computing. There are 22 articles in this book given as Invited Talks at the International Workshop on PDE Modeling and Computation held at IIT Madras during October 21-25, 2013. These selected articles showcasing the importance and challenges of PDE based mathematical modeling, analysis and computing. Covering a wide spectrum of applications, this Book is aimed at Masters and Ph.D. students aspiring to take up some challenges. Each article is carefully written, self contained and supported with up to date references. Contents - Mesh free method for numerical solution of the eikonal equation - A spline collection method for pricing options under the jump-diffusion model - An ale-based finite element method for the simulation of an impinging droplet on a hot surface - Multilevel augmentation method for parameter identification - StaRMAP- a second order staggered grid method for radiative transfer: application in radiotherapy - Exact controllability in domains with oscillating boundaries: homogenization - AC0 interior penalty method for an optimal control problem governed by the biharmonic operator - A multi-level finite element discretization for efficient solution of multidimensional population balance system - Meshfree numerical scheme for time dependent problems in fluid and continuum mechanics - On the wave equations of kirchhoff narasimha and carrier - Micromechanical modeling on non linear behaviour of 1-3 type piezocomposite - A meshfree approach for the numerical solution of straight fiber equations - Finite pointset method (FPM) for gas flows in slip regime - Comparison of RBF and hermite-RBF local schemes with variable (optimized) shape parameter - On the construction of dual gabor frame generators - Analysis of heatlines and entropy generation during natural convection within tilted square cavities - Modeling heat flow through glass fibre insulators - Evolutionary games and replicator dynamics - Deterministic ordinary differential equation models in population ecology, with special reference to indirect mutualism - Effect of surface piercing barriers on membrane- coupled gravity waves - Evolution of a pre-lens tear film after a blink - On enforcement of discrete maximum principle for coherence enhancing diffusion About the Author Prof. Dr. S. Sundar, Professor of Mathematics at the prestigious Indian Institute of Technology Madras is a DAAD Fellow and one of the four recipients of the Award “Alumni Ambassador of the City Kaiserslautern, Germany” and “Distinguished Alumni of Technical Universitaet Kaiserslautern, Germany” in the year 2012. Prof. Sundar is well known for his contribution in the broad field of Mathematical Modelling and Numerical Simulation. He has on his credit over 50 publications in high impact factor journals. He has guided over 10 Ph.D. students and several M.Tech./M.Sc. projects. Many of his Ph.D. and Masters students are in holding leading positions at various Industries across the World. Prof. Sundar is a Member of Department of Science and Technology (DST), Government of India – Programme Advisory Committee (Mathematical Sciences), Editorial Board Member of Journal of Indian Academy of Mathematics, Member of IIT Mandi Academic Council, Member of Board of Studies in several universities across India, to name a few.

Mathematical Logic - Ian Chiswell

Author

Ian Chiswell
Wilfrid Hodges

Cover Price : Rs 595.00

Imprint : Oxford University Press
ISBN : 0199548743
YOP : 2008

Binding : Paperback
Total Pages : 260
CD : No

About the Book :- - Based on the authors' extensive teaching on the subject - Practical examples are given for each idea as it is introduced - Methods and concepts are introduced intuitively in terms of actual mathematical practice, but then developed rigorously - Extensive exercises are presented along with selected solutions Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science. Contents :- Preface 1. Prelude 2. Informal natural deduction 3. Propositional logic 4. First interlude: Wason's Selection Task 5. Quantifier-free logic 6. Second interlude: The Linda Problem 7. First-order logic 8. Postlude A. The natural deduction rules B. Denotational semantics C. Solutions to some exercises Index. About the Authors :- Ian Chiswell, Queen Mary, University of London and Wilfrid Hodges, Queen Mary, University of London.

Mathematical Methods in Survival Analysis, Reliability and Quality of Life - Catherine Huber

Author

Catherine Huber
Nikolaos Limnios
Mounir Mesbah
Mikhail Nikulin

Cover Price : Rs 5,995.00

Imprint : Wiley
ISBN : 9788126553617
YOP : 2015

Binding : Hardback
Total Pages : 370
CD : No

Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory involved. This book aims to redress this situation: it includes 21 chapters divided into four parts: Survival analysis, Reliability, Quality of life, and Related topics. Many of these chapters are based on papers that were presented at the European Seminar on Mathematical Methods for Survival Analysis, Reliability and Quality of Life in 2006. Contents Preface PART I Chapter 1. Model Selection for Additive Regression in the Presence of Right-Censoring Elodie BRUNEL and Fabienne COMTE 1.1. Introduction 1.2. Assumptions on the model and the collection of approximation spaces 1.2.1. Non-parametric regression model with censored data 1.2.2. Description of the approximation spaces in the univariate case 1.2.3. The particular multivariate setting of additive models 1.3. The estimation method 1.3.1. Transformation of the data 1.3.2. The mean-square contrast 1.4. Main result for the adaptive mean-square estimator 1.5. Practical implementation 1.5.1. The algorithm 1.5.2. Univariate examples 1.5.3. Bivariate examples 1.5.4. A trivariate example 1.6. Bibliography Chapter 2. Non-parametric Estimation of Conditional Probabilities, Means and Quantiles under Bias Sampling Odile PONS 2.1. Introduction 2.2. Non-parametric estimation of p 2.3. Bias depending on the value of Y 2.4. Bias due to truncation on X 2.5. Truncation of a response variable in a non-parametric regression model 2.6. Double censoring of a response variable in a non-parametric model 2.7. Other truncation and censoring of Y in a non-parametric model 2.8. Observation by interval 2.9. Bibliography Chapter 3. Inference in Transformation Models for Arbitrarily Censored and Truncated Data Filia VONTA and Catherine HUBER 3.1. Introduction 3.2. Non-parametric estimation of the survival function S 3.3. Semi-parametric estimation of the survival function S 3.4. Simulations 3.5. Bibliography Chapter 4. Introduction of Within-area Risk Factor Distribution in Ecological Poisson Models Lea FORTUNATO, Chantal GUIHENNEUC-JOUYAUX, Dominique LAURIER,Margot TIRMARCHE, Jacqueline CLAVEL and Denis HEMON 4.1. Introduction 4.2. Modeling framework 4.2.1. Aggregated model 4.2.2. Prior distributions 4.3. Simulation framework 4.4. Results 4.4.1. Strong association between relative risk and risk factor, correlated within-area means and variances (mean-dependent case) 4.4.2. Sensitivity to within-area distribution of the risk factor 4.4.3. Application: leukemia and indoor radon exposure 4.5. Discussion 4.6. Bibliography Chapter 5. Semi-Markov Processes and Usefulness in Medicine Eve MATHIEU-DUPAS, Claudine GRAS-AYGON and Jean-Pierre DAURES 5.1. Introduction 5.2. Methods 5.2.1. Model description and notation 5.2.2. Construction of health indicators 5.3. An application to HIV control 5.3.1. Context 5.3.2. Estimation method 5.3.3. Results: new indicators of health state 5.4. An application to breast cancer 5.4.1. Context 5.4.2. Age and stage-specific prevalence 5.4.3. Estimation method 5.4.4. Results: indicators of public health 5.5. Discussion 5.6. Bibliography Chapter 6. Bivariate Cox Models Michel BRONIATOWSKI, Alexandre DEPIRE and Ya’acov RITOV 6.1. Introduction 6.2. A dependence model for duration data 6.3. Some useful facts in bivariate dependence 6.4. Coherence 6.5. Covariates and estimation 6.6. Application: regression of Spearman’s rho on covariates 6.7. Bibliography Chapter 7. Non-parametric Estimation of a Class of Survival Functionals Belkacem ABDOUS 7.1. Introduction 7.2. Weighted local polynomial estimates 7.3. Consistency of local polynomial fitting estimators 7.4. Automatic selection of the smoothing parameter 7.5. Bibliography Chapter 8. Approximate Likelihood in Survival Models Henning LAUTER 8.1. Introduction 8.2. Likelihood in proportional hazard models 8.3. Likelihood in parametric models 8.4. Profile likelihood 8.4.1. Smoothness classes 8.4.2. Approximate likelihood function 8.5. Statistical arguments 8.6. Bibliography PART II Chapter 9.Cox Regression with Missing Values of a Covariate having a Non-proportional Effect on Risk of Failure Jean-Francois DUPUY and Eve LECONTE 9.1. Introduction 9.2. Estimation in the Cox model with missing covariate values: a short review 9.3. Estimation procedure in the stratified Cox model with missing stratum indicator values 9.4. Asymptotic theory 9.5. A simulation study 9.6. Discussion 9.7. Bibliography Chapter 10.Exact Bayesian Variable Sampling Plans for Exponential Distribution under Type-I Censoring Chien-Tai LIN, Yen-Lung HUANG and N. BALAKRISHNAN 10.1. Introduction 10.2. Proposed sampling plan and Bayes risk 10.3. Numerical examples and comparison 10.4. Bibliography Chapter 11. Reliability of Stochastic Dynamical Systems Applied to Fatigue Crack Growth Modeling Julien CHIQUET and Nikolaos LIMNIOS 11.1. Introduction 11.2. Stochastic dynamical systems with jump Markov process 11.3. Estimation 11.4. Numerical application 11.5. Conclusion 11.6. Bibliography Chapter 12. Statistical Analysis of a Redundant System with One Standby Unit Vilijandas BAGDONAVIC¡ IUS, Inga MASIULAITYTE and Mikhail NIKULIN 12.1. Introduction 12.2. The models 12.3. The tests 12.4. Limit distribution of the test statistics 12.5. Bibliography Chapter 13.A Modified Chi-squared Goodness-of-fit Test for the ThreeparameterWeibull Distribution and its Applications in Reliability Vassilly VOINOV, Roza ALLOYAROVA and Natalie PYA 13.1. Introduction 13.2. Parameter estimation and modified chi-squared tests 13.3. Power estimation 13.4. Neyman-Pearson classes 13.5. Discussion 13.6. Conclusion 13.7. Appendix 13.8. Bibliography Chapter 14.Accelerated Life Testing when the Hazard Rate Function has Cup Shape Vilijandas BAGDONAVIC¡ IUS, Luc CLERJAUD and Mikhail NIKULIN 14.1. Introduction 14.2. Estimation in the AFT-GW model 14.2.1. AFT model 14.2.2. AFT-Weibull, AFT-lognormal and AFT-GW models 14.2.3. Plans of ALT experiments 14.2.4. Parameter estimation: AFT-GW model 14.3. Properties of estimators: simulation results for the AFT-GW model 14.4. Some remarks on the second plan of experiments 14.5. Conclusion 14.6. Appendix 14.7. Bibliography Chapter 15. Point Processes in Software Reliability James LEDOUX 15.1. Introduction 15.2. Basic concepts for repairable systems 15.3. Self-exciting point processes and black-box models 15.4. White-box models and Markovian arrival processes 15.4.1. A Markovian arrival model 15.4.2. Parameter estimation 15.4.3. Reliability growth 15.5. Bibliography PART III Chapter 16. Likelihood Inference for the Latent Markov Rasch Model Francesco BARTOLUCCI, Fulvia PENNONI and Monia LUPPARELLI 16.1. Introduction 16.2. Latent class Rasch model 16.3. Latent Markov Rasch model 16.4. Likelihood inference for the latent Markov Rasch model 16.4.1. Log-likelihood maximization 16.4.2. Likelihood ratio testing of hypotheses on the parameters 16.5. An application 16.6. Possible extensions 16.6.1. Discrete response variables 16.6.2. Multivariate longitudinal data 16.7. Conclusions 16.8. Bibliography Chapter 17. Selection of Items Fitting a Rasch Model Jean-Benoit HARDOUIN and Mounir MESBAH 17.1. Introduction 17.2. Notations and assumptions 17.2.1. Notations 17.2.2. Fundamental assumptions of the Item Response Theory (IRT) 17.3. The Rasch model and the multidimensional marginally sufficient Rasch model 17.3.1. The Rasch model 17.3.2. The multidimensional marginally sufficient Rasch model 17.4. The Raschfit procedure 17.5. A fast version of Raschfit 17.5.1. Estimation of the parameters under the fixed effects Rasch model 17.5.2. Principle of Raschfit-fast 17.5.3. A model where the new item is explained by the same latent trait as the kernel 17.5.4. A model where the new item is not explained by the same latent trait as the kernel 17.5.5. Selection of the new item in the scale 17.6. A small set of simulations to compare Raschfit and Raschfit-fast 17.6.1. Parameters of the simulation study 17.6.2. Results and computing time 17.7. A large set of simulations to compare Raschfit-fast, MSP and HCA/CCPROX 17.7.1. Parameters of the simulations 17.7.2. Discussion 17.8. The Stata module “Raschfit” 17.9. Conclusion 17.10.Bibliography Chapter 18. Analysis of Longitudinal HrQoL using Latent Regression in the Context of Rasch Modeling Silvia BACCI 18.1. Introduction 18.2. Global models for longitudinal data analysis 18.3. A latent regression Rasch model for longitudinal data analysis 18.3.1. Model structure 18.3.2. Correlation structure 18.3.3. Estimation 18.3.4. Implementation with SAS 18.4. Case study: longitudinal HrQoL of terminal cancer patients 18.5. Concluding remarks 18.6. Bibliography Chapter 19. Empirical Internal Validation and Analysis of a Quality of Life Instrument in French Diabetic Patients during an Educational Intervention Judith CHWALOW, Keith MEADOWS, Mounir MESBAH, Vincent COLICHE and Etienne MOLLET 19.1. Introduction 19.2. Material and methods 19.2.1. Health care providers and patients 19.2.2. Psychometric validation of the DHP 19.2.3. Psychometric methods 19.2.4. Comparative analysis of quality of life by treatment group 19.3. Results 19.3.1. Internal validation of the DHP 19.3.2. Comparative analysis of quality of life by treatment group 19.4. Discussion 19.5. Conclusion 19.6. Bibliography 19.7. Appendices PART IV Chapter 20. Deterministic Modeling of the Size of the HIV/AIDS Epidemic in Cuba Rachid LOUNES, Hector DE ARAZOZA, Y.H. HSIEH and Jose JOANES 20.1. Introduction 20.2. The models 20.2.1. The k2X model 20.2.2. The k2Y model 20.2.3. The k2XY model 20.2.4. The k2 XYX+Y model 20.3. The underreporting rate 20.4. Fitting the models to Cuban data 20.5. Discussion and concluding remarks 20.6. Bibliography Chapter 21.Some Probabilistic Models Useful in Sport Sciences Leo GERVILLE-REACHE, Mikhail NIKULIN, Sebastien ORAZIO, Nicolas PARIS and Virginie ROSA 21.1. Introduction 21.2. Sport jury analysis: the Gauss-Markov approach 21.2.1. Gauss-Markov model 21.2.2. Test for non-objectivity of a variable 21.2.3. Test of difference between skaters 21.2.4. Test for the less precise judge 21.3. Sport performance analysis: the fatigue and fitness approach 21.3.1. Model characteristics 21.3.2. Monte Carlo simulation 21.3.3. Results 21.4. Sport equipment analysis: the fuzzy subset approach 21.4.1. Statistical model used 21.4.2. Sensorial analysis step 21.4.3. Results 21.5. Sport duel issue analysis: the logistic simulation approach 21.5.1. Modeling by logistic regression 21.5.2. Numerical simulations 21.5.3. Results 21.6. Sport epidemiology analysis: the accelerated degradation approach 21.6.1. Principle of degradation in reliability analysis 21.6.2. Accelerated degradation model 21.7. Conclusion 21.8. Bibliography Appendices A. European Seminar: Some Figures A.1. Former international speakers invited to the European Seminar A.2. Former meetings supported by the European Seminar A.3. Books edited by the organizers of the European Seminar A.4. Institutions supporting the European Seminar (names of colleagues) B. Contributors Index Catherine Huber is an Emeritus professor at Université de Paris René Descartes, France. Nikolaos Limnios is a professor at the University of Technology of Compiègne, France. Mounir Mesbah is a professor at the Université Victor Segalen, Bordeaux 2, France.

Probability Theory - Yuan Shih Chow

Author

Yuan Shih Chow
Henry Teicher

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 8181281373
YOP : 2004
Edition : 2004

Binding : Paperback
Total Pages : 490
CD : No

DESCRIPTION Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familiar with measure theory using the guidelines given. Special features include: A comprehensive treatment of the law of the iterated logarithm * The Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof * Development and applications of the second moment analogue of Walds equation * Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence in the central limit theorem * Complete discussion, including central limit theorem, of the random casting of r balls into n cells * Recent martingale inequalities * Cram r-L vy theorem and factor-closed families of distributions. CONTENTS Classes of Sets, Measures,and Probability Spaces.- Binomial Random Variables.- Independence.- Integration in a Probabilty Space.- Sums of Independent Random Variables.- Measure Extensions, Lebesgue-Stieltjes Measure, Kolmogorov Consistency Theorem.- Conditional Expectation, Conditional Independence, Introduction to Martingales.- Distribution Functions and Characteristic Functions.- Central Limit Theorems.- Limit Theorems for Independent Random Variables.- Martingales.- Infinitely Divisible Laws.

Probability and Numerical Methods,3rd ed. - J. P. Singh

Author

J. P. Singh

Cover Price : Rs 275.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127512
YOP : 2015

Binding : Paperback
Total Pages : 408
CD : No

About the Book The third edition of probability and Numerical Methods is the result of the enthusiastic reception given to the earlier edition received from students and teachers, who are the end users of this book. The book covers the complete syllabus of BCA, Semester IV of GGSIP University. It introduces Probability and Numerical Methods at undergraduate level in a simplified manner. Salient features • Text is self-explanatory and the language is vivid and lucid. • Contains numerous examples that illustrate the basic as well as high level concepts of the concerned topic. • Additional questions provided in all the chapters for practice. • Most of the questions conform to the trend in which the questions appear in GGSIP University. Contents 0.Elementary Concepts 1. Combinatorics: Permutation, Combination and Binomial Theorem 2. Probability-I 3. Probability-II 4. Random Variable and Mathematical Expectations 5. Discrete Probability Distributions 6. Normal Distribution 7. Finite Difference 8. Interpolation 9. Solution of Algebraic and Transcendental Equations 10. Solution of Linear Simultaneous Equations 11. Numerical Differentiation and Integration Tables,End Term Examination About the Author J.P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has been teaching experience of 14 years and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi. His areas of interest include Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation.

GUIDE TO ABSTRACT ALGEBRA - CAROL WHITEHEAD

Author

CAROL WHITEHEAD

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan
ISBN : 0230574182
YOP : 2007
Edition : 2007

Binding : Paperback
Total Pages : 224
CD : No

DESCRIPTION:- Guide to Abstract Algebra is a comprehensive and accessible text covering the basic topics of an introductory abstract algebra course. New concepts are introduced gradually and illustrated by a variety of worked examples. New features in this second edition are:- · Two new chapters on Number Systems and Polynomials · Proofs by induction are introduced through a new section on sequences and recurrence relations · Fully updated to reflect the needs of today's first year undergraduate students This book is ideal for first year undergraduate courses in Mathematics or Computer Science. CONTENTS:- Glossary of symbols Preface to the second edition 1. Sets 2. Relations 3. Mappings 4. The Integers 5. Number Systems 6. Polynomials Suggestions for Further Reading Index. ABOUT THE AUTHOR:- CAROL WHITEHEAD has considerable experience of teaching mathematics at higher education level and is the author of a number of research papers in discrete mathematics.

Pattern Recognition Algorithms for Data Mining - Sankar K. Pal, Pabitra Mitra

Author

Sankar K. Pal
Pabitra Mitra

Cover Price : Rs 1,995.00

Imprint : CRC Press
ISBN : 9781498797764
YOP : 2016

Binding : Hardback
Total Pages : 272
CD : No

Reviews:- Pattern Recognition Algorithms in Data Mining is a book that commands admiration. Its authors, Professors S.K. Pal and P. Mitra are foremost authorities in pattern recognition, data mining, and related fields. Within its covers, the reader finds an exceptionally well-organized exposition of every concept and every method that is of relevance to the theme of the book. There is much that is original and much that cannot be found in the literature. The authors and the publisher deserve our thanks and congratulations for producing a definitive work that contributes so much and in so many important ways to the advancement of both the theory and practice of recognition technology, data mining, and related fields. The magnum opus of Professors Pal and Mitra is must-reading for anyone who is interested in the conception, design, and utilization of intelligent systems. - from the Foreword by Lotfi A. Zadeh, University of California, Berkeley, USA. The book presents an unbeatable combination of theory and practice and provides a comprehensive view of methods and tools in modern KDD. The authors deserve the highest appreciation for this excellent monograph. - from the Foreword by Zdzislaw Pawlak, Polish Academy of Sciences, Warsaw. This volume provides a very useful, thorough exposition of the many facets of this application from several perspectives. I congratulate the authors of this volume and I am pleased to recommend it as a valuable addition to the books in this field. - from the Forword by Laveen N. Kanal, University of Maryland, College Park, USA. About the Book:- Pattern Recognition Algorithms for Data Mining addresses different pattern recognition (PR) tasks in a unified framework with both theoretical and experimental results. Tasks covered include data condensation, feature selection, case generation, clustering/classification, and rule generation and evaluation. This volume presents various theories, methodologies, and algorithms, using both classical approaches and hybrid paradigms. The authors emphasize large datasets with overlapping, intractable, or nonlinear boundary classes, and datasets that demonstrate granular computing in soft frameworks. Organized into eight chapters, the book begins with an introduction to PR, data mining, and knowledge discovery concepts. The authors analyze the tasks of multi-scale data condensation and dimensionality reduction, then explore the problem of learning with support vector machine (SVM). They conclude by highlighting the significance of granular computing for different mining tasks in a soft paradigm. Contents:- Foreword. Preface. List of Tables. List of Figures. Introduction. Multiscale data condensation. Unsupervised feature selection. Active learning using support vector machine. Rough-fuzzy case generation. Rough-fuzzy clustering. Rough self-organizing map. Classification, rule generation and evaluation using modular rough-fuzzy MLP. Appendices. References. Index. About the Authors.

Textbook of Graph Theory - R. Balakrishnan

Author

R. Balakrishnan
K. Ranganathan

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 9781493975174
YOP : 2017

Binding : Paperback
Total Pages : 240
CD : No

About the Book:- Graph theory has experienced a tremendous growth during the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. This book aims to provide a solid background in the basic topics of graph theory. It covers Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices and a concrete application of triangulated graphs. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics. It can be used in an advanced undergraduate course or a beginning graduate course in graph theory. Contents:- Basic Results.- Directed Graphs.- Connectivity.- Trees.- Independent Sets and Matchings.- Eulerian and Hamiltonian Graphs.- Graph Colourings.- Planarity.- Triangulated Graphs.- Applications.

Functional Analysis - Kosaku Yosida

Author

Kosaku Yosida

Cover Price : Rs 895.00

Imprint : Springer
ISBN : 9783662559291
YOP : 2017

Binding : Paperback
Total Pages : 504
CD : No

TABLE OF CONTENTS Preliminaries.- Semi-norms.- Applications of the Baire-Hausdorff Theorem.- The Orthogonal Projection and F. Riesz' Representation Theorem.- The Hahn-Banach-Theorems.-Strong Convergence and Weak Convergence.- Fourier Transform and Differential Equations.- Dual Operators.- Resolvent and Spectrum.- Analytical Theory of Semi-groups.- Compact Operators.- Normed Rings and Spectral Representation.- Other Representation Theorems in Linear Spaces.- Ergodic Theory and Diffusion Theory.- The Integration of the Equations of Evolution. ABOUT THE AUTHOR Kôsaku Yosida (7.2.1909-20.6.1990) was born in Hiroshima, Japan. After studying mathematics a the University of Tokyo he held posts at Osaka and Nagoya Universities before returning to the University of Tokyo in 1955. Yosida obtained important and fundamental results in functional analysis and probability. He is best remembered for his joint work with E. Hille which brought forth a theory of semigroups of operators successfully applied to diffusion equations, Markov processes, hyperbolic equations and potential theory. His famous textbook on functional analysis was published in 6 distinct editions between 1965 and 1980.

CLASSIC ALGEBRA , INDIAN REPRINT - P.M. COHN (EX)

Author

P.M. COHN

Cover Price : Rs 3,995.00

Imprint : Wiley India
ISBN : 9788126540679
YOP : 2013

Binding : Hardback
Total Pages : 442
CD : No

Fundamental to all areas of mathematics, algebra provides the cornerstone for the students development. The concepts are often intuitive, but some can take years of study to fully absorb. For over twenty years, the authors classic three-volume set, Algebra, has been regarded by many as the most outstanding introductory work available. This work, Classic Algebra, combines a fully updated Volume 1 with the essential topics from Volumes 2 and 3, and provides a self-contained introduction to the subject. In addition to the basic concepts, advanced materials is introduced, giving the reader an insight into more advanced algebraic topics. The clear presentation style gives this book the edge over others on the subject. Undergraduates studying first courses in algebra will benefit from the clear exposition and perfect balance of theory, examples and exercises. The book provides a good basis for those studying more advanced algebra courses. • Complete and rigorous coverage of the important basic concepts • Topics covered include sets, mappings, groups, matrices, vector spaces, fields, rings and modules • Written in a lucid style, with each concept carefully explained • Introduces more advanced topics and suggestions for further reading • Contains over 800 exercises, including many solutions "There is no better textbook on algebra than the volumes by Cohn" - Walter Benz, Universität Hamburg, Germany Contents 1. Sets and Mappings. 2. Integers and Rational Numbers. 3. Groups. 4. Vector Spaces and Linear Mappings. 5. Linear Equations. 6. Rings and Fields. 7. Determinants. 8. Quadratic Forms. 9. Further Group Theory. 10.Rings and Modules. 11.Normal Forms for Matrices. Appendices. Solutions to the Exercises. Further Reading. Some Frequently Used Notations. Index.

GUIDE TO MECHANICS - Phil Dyke

Author

Phil Dyke
Roger Whitworth

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan
ISBN : 0230574168
YOP : 2007
Edition : 2007

Binding : Paperback
Total Pages : 360
CD : No

DESCRIPTION:- A sound knowledge of Mechanics is fundamental to an understanding of much of physics and engineering. This book takes the reader through the fundamentals of the subject in as informal a manner as possible, without sacrificing mathematical rigour. The second edition has new material on orbits, rigid body mechanics and non linear dynamics to produce a more comprehensive text that serves the needs of undergraduate students of mathematics, physics and engineering. CONTENTS:- Preface to Second Edition Kinematics Forces Forces as a Vector Collisions Motion Under Gravity Circular Motion Rotating Axes Vibrations Orbits Introduction to Rigid Body Dynamics Variable Mass Problems Nonlinear Dynamics Answers Index. ABOUT THE AUTHORS:- PHILIP P.G.DYKE is an experienced author with over 40 publications, including 8 textbooks ranging from mathematics and mechanics to marine science. He has over 30 years' lecturing experience in higher education, and has taught students across the ability range. Since 1985 he has been Professor of Applied Mathematics and Head of the School of Mathematics and Statistics at the University of Plymouth. ROGER WHITWORTH is Head of Mathematics at Droitwich High School.

An Introduction to Number Theory - Graham Everest

Author

Graham Everest
Thomas Ward

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181288035
YOP : 2007

Binding : Paperback
Total Pages : 302
CD : No

DESCRIPTION:- An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject. In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory. A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography. Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to learn some of the big ideas in number theory. CONTENTS:- A Brief History of Prime.- Diophantine Equations.- Quadratic Diophantine Equations.- Recovering the Fundamental Theorem of Arithmetic.- Elliptic Curves.- Elliptic Functions.- Heights.- The Riemann Zeta Function.- The Functional Equation of the Riemann Zeta Function.- Primes in an Arithmetic Progression.- Converging Streams.- Computational Number Theory.- References.- Index.

Essential Mathematical Biology - Nicholas F Britton

Author

Nicholas F Britton

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 8181281810
YOP : 2004

Binding : Paperback
Total Pages : 336
CD : No

DESCRIPTION Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology. A background in calculus and differential equations is assumed, although the main results required are collected in the appendices. A dedicated website at www.springer.co.uk/britton/ accompanies the book and provides further exercises, more detailed solutions to exercises in the book, and links to other useful sites. TABLE OF CONTENTS Single Species Population Dynamics Population Dynamics of Interacting Species Infectious Diseases Population Genetics and Evolution Biological Motion.- Molecular and Cellular Biology.- Pattern Formation Tumour Modelling.- Further Reading Some Techniques for Difference Equations Some Techniques for Ordinary Differential Equations Some Techniques for Partial Differential Equations Non-negative Matrices Hints for Exercises Index. WRITTEN FOR 3rd and 4th year undergraduate students of mathematics / mathematical biology, lecturers, postgraduate students, researchers, mathematically literate biologists KEYWORDS -Cancer modelling -Mathematical biology -Mathematical modelling -Molecular and cellular biology -Pattern formation -Population dynamics -Population genetics and evolution

Linear Algebra - Klaus Janich

Author

Klaus Janich

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 818128187X
YOP : 2004

Binding : Paperback
Total Pages : 206
CD : No

DESCRIPTION This book covers the material of an introductory course in linear algebra: sets and maps, vector spaces, bases, linear maps, matrices, determinants, systems of linear equations, Euclidean spaces, eigenvalues and eigenvectors, diagonalization of self-adjoint operators, and classification of matrices. The book is written for beginners. Its didactic features (the "book within a book" and multiple choice tests with commented answers) make it especially suitable for self-study. TABLE OF CONTENTS 1. Sets and Maps 2. Vector Spaces 3. Dimension 4. Linear Maps 5. Matrix Calculus 6. Determinants 7. Systems of Linear Equations 8. Euclidean Vector Spaces 9. Eigenvalues 10. The Principal Axes Tranformation 11. classification of Matrices 12. Answer to the tests References Index.

A Beginner's Guide to Finite Mathematics - W D Wallis

Author

W D Wallis

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181282175
YOP : 2004

Binding : Paperback
Total Pages : 356
CD : No

DESCRIPTION This concise text takes a distinctly applied approach to finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which provides the foundation for elementary probability theory; this, in turn, leads to basic statistics. Graph theory is defined, with particular emphasis on its use in mathematical modeling. Matrices and vectors are discussed, along with several elementary commercial applications. The book concludes with an introduction to linear programming, including the simplex method and duality. Ample examples and illustrations are provided throughout; each section contains two sets of problems, with solutions provided for the first set. Requiring little mathematical background beyond high school algebra, the text will be especially useful for business and liberal arts majors. Its straightforward treatment of the essential concepts in finite mathematics will appeal to a wide audience of students and teachers. CONTENTS Preface Numbers and Sets Counting Probability Relations and Functions Graph Theory Matrices Linear Programming Bibliography Answers to Group A Exercises Index.

Differential and Integral Equations - Peter J. Collins

Author

Peter J. Collins

Cover Price : Rs 795.00

Imprint : Oxford University Press
ISBN : 0195695828
YOP : 2008

Binding : Paperback
Total Pages : 384
CD : No

About the Book :- Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis. Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'. Contents :- Preface How to use this book Prerequisites 1. Integral equations and Picard's method 2. Existence and uniqueness 3. The homogeneous linear equation and Wronskians 4. The non-homogeneous linear equation: Variations of parameters and Green's functions 5. First-order partial differential equations 6. Second-order partial differential equations 7. The diffusion and wave equations and the equation of Laplace 8. The Fredholm alternative 9. Hilbert-Schmidt theory 10. Iterative methods and Neumann series 11. The calculus of variations 12. The Sturm-Liouville equation 13. Series solutions 14. Transform methods 15. Phase-plane analysis Appendix: The solution of some elementary ordinary differential equations Bibliography Index. About the Author :- Peter Collins has taught differential and integral equations for 40 years and has held posts in universities in the United Kingdom, United States, France and New Zealand. He is currently Senior Research Fellow of St Edmund Hall, Oxford, and Head of the Analytic Topology Research Group at Oxford University's Mathematical Institute.

GUIDE TO MATHEMATICAL METHODS - JOHN GILBERT

Author

JOHN GILBERT
CAMILLA JORDAN

Cover Price : £ 9.99

Imprint : Palgrave / Macmillan
ISBN : 0230574144
YOP : 2007
Edition : 2007

Binding : Paperback
Total Pages : 440
CD : No

DESCRIPTION A second edition of this text for science and engineering undergraduates which introduces the mathematical techniques and tools needed to solve the mathematical problems they will face on the first year of their course. Updated and revised by Camilla Jordan, the book now has additional examples and 'Aims and Objectives' sections. As with other titles in the Mathematical Guides series, this book is designed to enable students to acquire confidence and provides a solid foundation for further study. CONTENTS Preface Symbols, notation and Greek letters Preliminaries Functions Differentiation Further Functions Applications of Differentiation Integration Further Integration Linear Equations and Matrices Vectors Functions of Two Variables Line Integrals Double Integrals Complex Numbers Differential Equations. ABOUT THE AUTHORS JOHN GILBERT is Senior Lecturer in Mathematics at Lancaster University. CAMILLA JORDAN is a Staff Tutor in the Mathematics and Computing Faculty of the Open University.

Theory and Applications of Partial Functional Differential Equations - Jianhong Wu

Author

Jianhong Wu

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181283198
YOP : 2005

Binding : Paperback
Total Pages : 443
CD : No

DESCRIPTION Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations. CONTENTS Introduction.- Preliminaries.- Existence and compactness of solution semiflows. Generators and decomposition of state spaces for linear systems.- Nonhomogenous systems and linearized stability.- Invariant manifolds of nonlinear systems.- Hopf Bifurcations.-Small and large diffusivity.- Invariance, comparison, lower and upper solutions.- Convergence, monotononicity and contracting rectangles.- Dispativeness, exponential growth and invariance principles.- Travelling wave solutions.- References.- Index.

Basic Principles of the Finite Element Method - K M Entwistle

Author

K M Entwistle

Cover Price : Rs 695.00

Imprint : Woodhead
ISBN : 190265353X
YOP : 2005

Binding : Paperback
Total Pages : 204
CD : No

DESCRIPTION The objective of this book is to provide and introductory text that lays out the basic theory of the finite element method in a form that will be comprehensible to materials scientists. It presents the basic ideas in a sequential and measured fashion, avoiding the use of specialist vocabulary that is not clearly defined. The basic principles are illustrated by a diversity of examples that serve to reinforce the particular aspects of the theory. CONTENTS About matrices; The stiffness matrix; One-dimensional finite element analysis; Energy principles in finite element analysis; Finite elements that form part of a continuum; Finite element analysis using higher order elements; Worked examples applying the theory of section 7.2 to calculate the stresses in a loaded tapered sheet; A cautionary epilogue.

Structure Determination of Organic Compounds : Tables of Spectral Data - E. Pretsch

Author

E. Pretsch
P. Buhlmann
C. Affolter

Cover Price : Rs 895.00

Imprint : Springer
ISBN : 818128383X
YOP : 2006

Binding : Paperback
Total Pages : 460
CD : Yes

DESCRIPTION This volume presents in the form of texts, tables, charts and graphs a modern compilation of spectroscopic reference data for IR, UV/Vis, 1H- and 13C-NMR, MS (incl. prototype spectra of almost every important class of organic compounds and spectra of MALDI and FAB matrix materials) and is intended as a short textbook and a hands-on guide for interpreting experimental spectral data and elucidating the chemical structure of the respective compound behind it. The concise texts include special chapters on fragmentation rules in mass spectrometry and on currently used multipulse and 2-D NMR techniques. The book is primarily designed for students to be used during courses and exercises. The use of the book requires only basic knowledge of spectroscopic techniques, but is structured in such a way that it will support practitioners routinely faced with the task of interpreting such spectral information, and it will serve as data reference for specialists in the fields. CONTENTS 1 Introduction 2.Summary Tables 3.Combination Tables 4.13C NMR Spectroscopy 5.1H NMR Spectroscopy 6.IR Spectroscopy 7. Mass Spectroscopy 8.UV/Vis Spectroscopy Subject Index.

Introductory Complex Analysis - Richard A. Silverman

Author

Richard A Silverman

Cover Price : $ 17.95

Imprint : Dover
ISBN : 9780486946862
YOP : 2016

Binding : Paperback
Total Pages : 400
CD : No

About the Book Introductory Complex Analysis is a scaled-down version of A. I. Markushevich's masterly three-volume "Theory of Functions of a Complex Variable." Dr. Richard Silverman, the editor and translator of the original, has prepared this shorter version expressly to meet the needs of a one-year graduate or undergraduate course in complex analysis. In his selection and adaptation of the more elementary topics from the original larger work, he was guided by a brief course prepared by Markushevich himself. The book begins with fundamentals, with a definition of complex numbers, their geometric representation, their algebra, powers and roots of complex numbers, set theory as applied to complex analysis, and complex functions and sequences. The notions of proper and improper complex numbers and of infinity are fully and clearly explained, as is stereographic projection. Individual chapters then cover limits and continuity, differentiation of analytic functions, polynomials and rational functions, Mobius transformations with their circle-preserving property, exponentials and logarithms, complex integrals and the Cauchy theorem , complex series and uniform convergence, power series, Laurent series and singular points, the residue theorem and its implications, harmonic functions (a subject too often slighted in first courses in complex analysis), partial fraction expansions, conformal mapping, and analytic continuation. Elementary functions are given a more detailed treatment than is usual for a book at this level. Also, there is an extended discussion of the Schwarz-Christolfel transformation, which is particularly important for applications. There is a great abundance of worked-out examples, and over three hundred problems (some with hints and answers), making this an excellent textbook for classroom use as well as for independent study. A noteworthy feature is the fact that the parentage of this volume makes it possible for the student to pursue various advanced topics in more detail in the three-volume original, without the problem of having to adjust to a new terminology and notation . In this way, IntroductoryComplex Analysis serves as an introduction not only to the whole field of complex analysis, but also to the magnum opus of an important contemporary Russian mathematician. About the Author Richard A. Silverman: Dover's Trusted Advisor Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the 1970s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century. These titles include (but are by no means limited to): Special Functions and Their Applications (Lebedev); Methods of Quantum Field Theory in Statistical Physics (Abrikosov, et al); An Introduction to the Theory of Linear Spaces, Linear Algebra, and Elementary Real and Complex Analysis (all three by Shilov); and many more. During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions.

Theory of Transforms with Applications - Vinod Mishra

Author

Vinod Mishra

Cover Price : Rs 1,995.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789385462603
YOP : 2017

Binding : Hardback
Size : 6.25" X 9.50"
Total Pages : 368
CD : No

About the Book Mathematical transforms play an important role in solving ordinary and partial differential equations, integral and integro-differential equations, difference equations and problems arising in applied science and engineering. Bulk of these problems are solved using Fourier, Laplace, Mellin and Hankel transforms. Many of the problems unresolved by existing classical techniques due to the nature and complexities involved. In such a scenario, implementation of the approximation or numerical techniques as Discrete and Fast Fourier transform and numerical inversion of Laplace transform become a necessity. Z transform is best suited for analyzing electrical signals. Little known Legendre transform plays significant role in thermodynamics and classical mechanics. This book peeps into continuous and discrete version of Fourier and Laplace transforms. Mellin, Hankel and Legendre transforms in continuous version have been placed next; while the Z transform occupies the last chapter. Each transform is related to one or more of these transforms. A wide range of applications and problems are covered in physical, engineering and medical world including Dirichlet boundary value problem, Sturm-Liouville problem, transfer function, classical, statistical and quantum mechanics, state space equations, electrical signals, heat, wave and steady state equations, Poisson equation, probability density function and thermodynamics. The case studies include problems from mechanics, population dynamics, seismology, elasticity and medicine. The book presented with a view of philosophy of learning helps the readers to have access to advanced concepts through theory and varied applications in pedagogical way. Certain numerical inversion of Laplace transform and Legendre transform are distinctive. Historical development would not only provide the origin and growth of the concept but also excitement and insight of great scholars providing beautiful tools and perhaps could be inspirational factor to the readers. Lucid style of presentation and rigorous mathematical approach are the key features. Proofs of theorems and lemmas have been presented wherever necessary. Few case studies and examples of significance have been included to make the concept understandable. The book is suitable for both UG/PG and B.Tech./M.Tech. students of Mathematics and Physics, practitioners, teachers and research scholars in the field of mathematics, physics and engineering. Contents Chapter 1: Fourier Series Chapter 2: Continuous Fourier Transform Chapter 3: Discrete and Fast Fourier Transform Chapter 4: Laplace Transform Chapter 5: Numerical Inverse Laplace Transform Chapter 6: Mellin Transform Chapter 7: Hankel Transform Chapter 8: Legendre Transform Chapter 9: Z Transform About the Author Currently, a Professor (former Head) at the Department of Mathematics, at Sant Longowal Institute of Engineering and Technology (Deemed University established by MHRD, Govt. of India), Longowal, Punjab, he has been active member of Senate and Board of Studies at the same institute and is associated with various mathematical societies in India and abroad. He is also the ‘Fellow’ of prestigious Indian Institute of Advanced Study based at Shimla where he submitted a research monograph also. He enjoys nearly twenty three years of regular teaching experience of undergraduate and postgraduate courses in higher education in science, technology and research at the grass-root and advanced levels of mathematical science and has brought innumerable publications in the field of history & education of mathematics, wavelet analysis of numerical problems and numerical inverse Laplace transforms. He has chaired eight technical sessions and delivered twelve invited lectures during national and international conferences in India and overseas.

Introduction to Mathematics for Life Scientists 3/ed - E. Batschelet, Reprint 2015, Best Seller

Author

E. Batschelet

Cover Price : Rs 995.00

Imprint : Springer
ISBN : 9788181280848
YOP : 2015

Binding : Paperback
Total Pages : 662
CD : No

DESCRIPTION The book is suitable both for use as a classroom textbook and for self teaching. This third edition includes more problems and solutions as well as many worked examples. The chapters on calculus and linear algebra have been particularly expanded and the work has been amended throughout following suggestions from leading biomathematicians. Practical applications include: electrocardiogram, biological rhythm, flow of blood in blood vessels, psychophysical scaling and various problems from genetics and systems analysis. From a review: "For research workers in the biomedical field who feel a need for freshening up their knowledge in mathematics, but so far have always been frustrated by either too boring textbooks, there is now exactly what they would like to have: an easy to read introduction. This book is highly motivating for practical workers because only those mathematical techniques are offered for which there is an application in the life sciences. The reader will find it stimulating that each tool described is immediately exemplified by problems from latest publications. CONTENTS Chapter 1. Real Numbers Chapter 2. Sets and Symbolic Logic Chapter 3. Relations and Functions Chapter 4. The Power Function and related functions Chapter 5. Periodic Functions Chapter 6. Exponential and Logarithmic Functions I Chapter 7. Graphical Methods Chapter 8. Limits Chapter 9. Differential and Integral Calculus Chapter 10. Exponential and Logarithmic Functions II Chapter 11. Ordinary Differential Equations Chapter 12. Functions of Two or more Independent Variables Chapter 13. Probability Chapter 14. Matrices and Vectors Chapter 15. Complex Numbers Appendix (Tables A to K) Solutions to odd Numbered Problems References Author and Subject Index.

Optimization : Linear Programming 2015 - B. N. Mishra

Author

B. N. Mishra
B. K. Mishra

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9788180521256
YOP : 2017

Binding : Paperback
Total Pages : 318
CD : No

About the Book Optimization is a comprehensive textbook which has grown out of the collective experience of the authors in teaching the course over the years. The introductory text provides undergraduate and graduate students with a concise and practical introduction to the primary concepts and techniques of optimization. With a strong emphasis on basic concepts and techniques throughout, the book explains the theory behind each technique as simply as possible, along with illustrations and worked examples. Salient Features • A rigorous discussion on linear programming and its duality including model formulation. Additional solved examples and multi choice objective questions included at the last. • Theory of convex sets discussed. • Formulation of Transportation problem and methods of solution discussed, including optimality test. • Assignment problem formulated and discussed. • Emphasis on Degeneracy and game theory. Pedagogical Features • Simple, lucid and easily retainable language. • Illustrative examples • Unsolved problems. • More real life applications • Detailed index. CONTENTS Preface, 1. Linear Programming, 2. Simplex Method, 3. Convex Sets, 4. Transportation, 5. Assignment Problems, 6. Theory of games, 7. Duality Theory, 8. Degeneracy. About the Author Dr. B.N.Mishra has retired as a University Professor and Head Department of Mathematics, Vinoba Bhave University, Hazaribag, Jharkhand. His research areas are in the field of Fluid Mechanics, Bio-Mathematics, and Vedic Mathematics. He has published several research papers in the journals of national as well as international repute. He has produced 20 Ph.D.'s and one D.Sc. He has a vast experience in teaching undergraduate and postgraduate students. He has taught the course Operations Research for more than 25 years. He has also published several books. Dr. Bimal Kumar Mishra is an Assistant Professor in the Mathematics Group, Birla Institute of Technology and Science, Pilani, Rajasthan. He got his M.Sc. Degree in Operational Research from University of Delhi and also M.Sc. Degree in Mathematics .He has published more then thirty five research papers in journals of national and international repute. His research areas are in the field of Mathematical Modeling on Blood Flow, Environmental Pollution, Population Dynamics and Computer Viruses.

Topology, Reprint 2011 - Klaus Janich

Author

Klaus Janich

Cover Price : Rs 495.00

Imprint : Springer
ISBN : 8181284984
YOP : 2011

Binding : Paperback
Total Pages : 200
CD : No

DESCRIPTION This is an intellectually stimulating, informal presentation of those parts of point set topoloty that are of importance to the nonspecialist . In his presentation and through many illustrations, the author strongly appeals to the intuition of the reader, presenting many examples and situations where the understanding of elementary topological questions will lead to much deeper and more advanced problems in topology and geometry. CONTENTS Introduction Chapter 1 Fundamental Concepts Chapter 2 Topological Vector Spaces Chapter 3 The Quotient Topology Chapter 4 Completion of Metric Spaces Chapter 5 Homotopy Chapter 6 The Two Countability Axioms Chapter 7 CW – Complexes Chapter 8 Construction pf Continuous Functions on Topological Spaces Chapter 9 Covering Prices Chapter 10 The Theorem of Tychonoff Last Chapter Set Theory References Table of Symbols Index

Mathematical Modeling : Application, Issues and Analysis - Bimal K. Mishra

Author

Bimal K. Mishra
Dipak K. Satpathi

Cover Price : Rs 795.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 8180521273
YOP : 2009

Binding : Paperback
Total Pages : 464
CD : No

Reprinted in 2008

About the Book :- Mathematical Modeling is a discipline, which helps in solving real life problems by shaping them into mathematical models. Process of Mathematical Modeling can be divided into three steps. 1. Defining the problem 2. Simplifying the problem by introducing certain assumptions and converting the problem into the mathematical equations. 3. Solving the mathematical equations and interpretation of the results. National Conference on Mathematical Modeling and Analysis provides discussions and insights of leading scientists, engineers and technocrats from all over the country. It includes papers in the areas of • Drug Design • Biological systems • Environmental Pollution • Fluid Mechanics • Applied Analysis With this coverage, the book would serve as a useful reference for scientists, engineers, technocrats and researchers. Contents :- Preface List of Contributors Section I: Drug Design Section II: Biological Systems Section III: Industrial Mathematics Section IV: Environmental Pollution Section V: Fluid Mechanics Section VI: Applied Analysis About the Editors Dr. Bimal Kumar Mishra is an Assistant Professor in the Mathematics Group, Birla Institute of Technology and Science, Pilani. He has published more then thirty research papers in journals of national and international repute. His research areas are in the field of Mathematical Modeling on Blood Flow, Environmental Pollution, Population Dynamics and Computer Viruses. Dr. Dipak Kumar Satpathi is an Assistant Professor in Mathematics Group, Birla Institute of Technology and Science, Pilani. He earned his Ph.D. degree from IIT Kanpur and his area of research is in the field of Biomechanics.

Calculus of One Variable - M.Thamban Nair, 2016

Author

M.Thamban Nair

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789383656950
YOP : 2015

Binding : Paperback
Total Pages : 320
CD : No

About the Book: The book is meant for a one-semester introductory course on Calculus of One Variable at the Bachelors levels of Science and Engineering programs. It provides clear understanding of the basic concepts of differential and integral calculus, and also introduces slightly advanced topics such as power series and Fourier series. The introduction of sequences and series as the first chapter of the book helps a great deal in the discussion of various other concepts in the later chapters. Key features: · Precise definitions of basic concepts are given. · Several motivating examples are provided for understanding the concepts and also for illustrating the results. · Proofs of theorems are given with sufficient motivation – not just for the sake of proving them alone. · Remarks in the text supply additional information on the topics under discussion. · Exercises are interspersed within the text for making the students attempt them while the lectures are in progress. · Large number of problems at the end of each chapter are meant as home-assignments. The student friendly approach of the exposition of the book would definitely be of great use not only for students, but also for the teachers of the course. About the Author: Dr. M. Thamban Nair, Professor of Mathematics at IIT Madras, is a Research Mathematician as well as a teacher for more than 25 years at the Post Graduate and Under Graduate level courses in mathematics. He taught Calculus courses to B.Tech students of IIT Madras many times since 1995. He has won the prestigious C.L. Chandana Award for Distinguished and Outstanding Contributions to Mathematics Research and Teaching in India for the year 2003. He was also a Post Doctor Fellow at University of Grenoble (France), Visiting Fellow/Professor at Australian National University (Australia), University of Kasiserslautern (Germany) and Sun Yat-sen University, Guangzhou (China). He published more than 65 research papers in national international journals, and also author of two books, one on Functional Analysis for M.Sc level and another on Linear Operator Equations for Post-MSc level. He gave several invited talks at various conferences in India and abroad, and also a mentor of INSPIRE program of DST.

ALGEBRA -I (A BASIC COURSE) - ASHA GAURI SHANKAR

Author

ASHA GAURI SHANKAR

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127888
YOP : 2015

Binding : Paperback
Total Pages : 448
CD : No

About the Book This book is designed as a textbook for the Undergraduate students. It meets the curriculum requirements of the Course I.2 Algebra I (DC-I) of the University of Delhi. This book is useful for students of any other University also who would like to study the topics covered in this book. It focuses on the introductory aspects of the course, supporting the theory with numerous Examples and Solved Problems. The text starts with equivalence relations, and goes on to functions. It explains the Principle of Mathematical Induction and also proves the Fundamental Theorem of Arithmetic. Complex numbers in polar form have also been introduced and the nth roots of unity have been explained in detail. Linear equations, linear transformations, matrices, eigenvalues and eigenvectors and vector spaces have also been covered. A unique feature is the glossary of the terms used in the text and summary of the chapters. The salient features of the book are: -Learning objectives given at the beginning of each chapter. -Concepts illustrated with examples. -Stepwise Proofs of Theorems and Solution of problems. -Emphasis on techniques of problem solving through numerous solved problems. -Graded Exercises. -Concepts reinforced by true/false questions. -Chapter-wise summary for ready reference. -Glossary of the terms used in the text. -Index for ready reference. -Answers to all the exercises and hints to difficult questions. About the Author Dr. Asha Gauri Shankar, earned her Ph.D. in Numerical Analysis from Imperial College of Science, Technology and Medicine, University of London as a Commonwealth Scholar. She also earned her Ph.D. in Topology from Chaudhary Charan Singh University. For over 4 decades, she has taught undergraduate and postgraduate students at the University of Delhi; Imperial College of Science, Technology and Medicine, London and the Institute of Advanced Studies, Meerut. She has to her credit research papers in national and international journals, several popular articles, a research level book “Numerical Integration of Differential Equations”, and three books for university students “Algebra I”, Pearson Education(2012); “Complex Numbers and Theory of Equations”, Anthem Press(2012), and “Group Theory ”, Pearson Education(2013). Her research interest is in Mathematics Education and Numerical Analysis. In September 2009, she was awarded “Teacher of Excellence” by the University of Delhi. She has also been awarded “Bharat Excellence Award ” and “Mahila Sree Award” by FFI and the Shiksha Rattan Puraskar by IIFS. Dr. Asha Gauri Shankar is currently an Associate Professor in the Department of Mathematics in Lakshmibai College, University of Delhi.

GUIDE TO ANALYSIS - MARY HART

Author

MARY HART

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan
ISBN : 0230574113
YOP : 2007
Edition : 2007

Binding : Paperback
Total Pages : 304
CD : No

DESCRIPTION This new edition aims to guide undergraduate students through the first year of their mathematics course. It provides a rigorous introduction to Analysis, which takes into account the difficulties students often face when making the transition from A-level mathematics to this higher level. Plenty of examples are provided, some of which have full, detailed solutions, and others which encourage the student to discover and investigate the ideas themselves. Hints are provided, but the book aims to build confidence and understanding in all topics. This second edition has two new substantial chapters, covering integration and powere series, and is updated throughout, taking into account changes in notation. CONTENTS Preface Introduction Numbers and Number Systems Sequences Infinite Series Functions Differentiable Functions Integration Power series Index ABOUT THE AUTHOR MARY HART is a lecturer in Pure Mathematics at Sheffield University.

GUIDE TO SCIENTIFIC COMPUTING - PETER R. TURNER

Author

PETER R. TURNER

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan
ISBN : 0230574175
YOP : 2007
Edition : 2007

Binding : Paperback
Total Pages : 312
CD : No

DESCRIPTION This book is a gentle and sympathetic introduction to many of the problems of scientific computing, and the wide variety of methods used for their solutions. It is ideal for students taking a first course in numerical mathematics who need a low level entry to the subject. It gives an appreciation of the need for numerical methods for the solution of different types of problem, and discusses basic approaches. For each of the problems, at least some mathematical justification and examples provide both practical evidence and motivations for the reader to follow. Practical justification of the methods is presented through computer examples and exercises. The book also includes an introduction to MATLAB, but the code used is not intended to exemplify sophisticated or robust pieces of software; it is purely illustrative of the methods under discussion. ☻ Includes appendix covering MATLAB basics ☻ Class-tested at the US Naval Academy and University of Lancaster ☻ No prior mathematical knowledge assumed beyond calculus CONTENTS Number Representations and Errors Iterative Solution of Equations Approximate Evaluation of Functions Interpolation Numerical Calculus Differential Equations Linear Equations MATLAB Basics Answers to Exercises . ABOUT THE AUTHORS PETER TURNER is a Professor in the Department of Mathematics at the US Naval Academy in Annapolis. He was awarded his PhD from the University of Sheffield and has extensive undergraduate teaching experience at the Universities of Sheffield, Lancaster and Maryland as well as at the US Naval Academy, where he has been responsible for introductory courses in scientific computing for more than a decade.

Advanced Graph Theory - S.K. Yadav

Author

S.K. Yadav

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789385462634
YOP : 2017

Binding : Paperback
Size : 6.25" X 9.50"
Total Pages : 302
CD : No

About the Book This book is designed to meet the syllabus requirements of the students of B.Sc. (H) (Math/Computer Sc./Physcial Sc), B.C.A/M.C.A., B.Tech.(Computer Sc., E.C.E., I.T.,), M.Tech(C.S.E./ I.T.), M.Sc.(Mathematics/C.S./Electronics) and other professional courses of various universities/institutions at home and abroad. The students of open and distance education courses will find the book most useful. Contents 1. Basics of Graph Theory 2. Trees 3. Planar Graphs 4. Directed Graphs 5. Matching and Covering 6. Colouring of Graphs 7. Colouring of Graphs 8. Enumeration and Pölya’s Theorem 9. Spectral Properties of Graphs 10. Spectral Properties of Graphs About the Author Dr. Santosh Kumar Yadav has been associated with academic and research activities for more than 25 years. He has been an active and dynamic administrator as Director (Academic and Research) at J.J.T. University, Rajasthan. As an academician he has taught under graduates and post graduate classes in different premire institutions including various colleges of Delhi University in different capacities. As a researcher, Dr. Yadav has guided more than 70 research scholars of different universities at home and abroad. As an author he has written 38 books and more than a century of self-learning materials of different universities. Dr.Yadav is editor of six well reputed international journals of research and life member of 26 reputed professional apex bodies of academics and research.

CONCRETE INTRODUCTION TO HIGHER ALGEBRA 2ND ED - Lindsay N. Childs (EX)

Author

Lindsay N. Childs

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 9788181284136
YOP :

Binding : Paperback
Total Pages : 544
CD : No

About the Book :- This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, error correction, integration, and especially to elementary and computational number theory. The later chapters include expositions of Rabin's probabilistic primality test, quadratic reciprocity, the classification of finite fields, and factoring polynomials over the integers. Over 1000 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix. Contents :- Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruence.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Fermat's and Euler's Theorems.- Applications of Fermat's and Euler's Theorems.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in Q[x].- Congruences and the CRT.- Fast Polynomial Multiplication.- Cyclic Groups and Cryptography.- Carmichael Numbers..- Quadratic Reciprocity.- Quadratic Applications.- Congruence Classes Modulo a Polynomial.- Homomorphism and Finite Fields.- BCH Codes.- Factoring in Z[x].- Irreducible Polynomials.- Answers and Hints to the Exercises.- References.- Index.

A Friendly Guide to Wavelets - Gerald Kaiser

Author

Gerald Kaiser

Cover Price : Rs 995.00

Imprint : Springer
ISBN : 8181283818
YOP : 2008

Binding : Paperback
Total Pages : 320
CD : No

Reviews :- "I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent... Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time." — Proceedings of the IEEE "It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one." — Computing Reviews "I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets." — Physics Today "This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing." — SIAM Review "The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field." — Mathematical Reviews About the Book :- This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption.

Applied Probability - Kenneth Lange

Author

Kenneth Lange

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181289544
YOP : 2008

Binding : Paperback
Total Pages : 318
CD : No

About the Book :- This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Contents :- Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material here for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. Finally, Chapters 12 and 13 develop the Chen-Stein method of Poisson approximation and connections between probability and number theory. About the Author :- Kenneth Lange is Professor of Biomathematics and Human Genetics and Chair of the Department of Human Genetics at the UCLA School of Medicine. He has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer-Verlag published his books Numerical Analysis for Statisticians and Mathematical and Statistical Methods for Genetic Analysis Second Edition, in 1999 and 2002, respectively.

Basic Stochastic Processes - Tomasz Zastawniak

Author

Tomasz Zastawniak
Zdzislaw Brzezniak

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181283279
YOP : 2005

Binding : Paperback
Total Pages : 240
CD : No

About the Book :- This book is a final year undergraduate text on stochastic processes, a tool used widely by statisticians and researchers working in the mathematics of finance. The book will give a detailed treatment of conditional expectation and probability, a topic which in principle belongs to probability theory, but is essential as a tool for stochastic processes. Although the book is a final year text, the author has chosen to use exercises as the main means of explanation for the various topics, and the book will have a strong self-study element. The author has concentrated on the major topics within stochastic analysis: martingales in discrete time and their convergence, Markov chains, stochastic process in continuous time, with emphasis on the Poisson process and Brownian motion, as well as Itô stochastic calculus including stochastic differential equations. The Springer Undergraduate Mathematics Series (SUMS) is a new series of guides, written for undergraduates in the Mathematical Sciences. The books cover the basics of each topic via explanatory text, examples and problems. Students can read and check their understanding of the text against fully worked solutions at the back of each chapter. Contents :- Preface 1. Review of Probability 2. Conditional Expectation 3. Martingales in Discrete Time 4. Martingale Inequalities and Convergence 5. Markov Chains 6. Stochastic Processes in Continuous Time 7. Itô stochastic Calculus Index.

Partial Differential Equations : Basic Theory - Michael E. Taylor

Author

Michael E. Taylor

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 8181284143
YOP : 2006

Binding : Paperback
Total Pages : 584
CD : No

About the Book :- This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. Contents :- Series Preface Introduction 1. Basic Theory of ODE and Vector Fields 2. The Laplace Equation and Wave Equation 3. Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE 4. Sobolev Spaces 5. Linear Elliptic Equations 6. Linear Evolution Equations A. Outline of Functional Analysis B. Manifolds, Vector Bundles, and Lie Groups Index.

Complex Analysis - John M. Howie, 2015

Author

John M. Howie

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 9788181282965
YOP : 2015

Binding : Paperback
Total Pages : 272
CD : No

About the Book :- Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. Contents :- Preface 1. What Do I Need to Know? 2. Complex Numbers 3. Prelude to Complex Analysis 4. Differentiation 5. Complex Integration 6. Cauchy’s Theorem 7. Some Consequences of Cauchy’s Theorem 8. Laurent Series and the Residue Theorem 9. Applications of Contour Integration 10.Further Topics 11.Conformal Mappings 12.Final Remarks 13.Solutions to Exercises Bibliography Index.

Real Analysis - J. P. Singh

Author

J. P. Singh

Cover Price : Rs 180.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 8180522709
YOP : 2009

Binding : Paperback
Total Pages : 368
CD : No

About the Book :- This book 'Real Analysis' is primarily designed for the undergraduate students of GGS Indraprastha University and reflects my understanding of the requirements of students. In addition, this book would be extremely useful for all the students studying Real Analysis at the undergraduate level at other Indian Universities. Some of the salient features of this book are :- • It covers the entire syllabus of BCA III sem of GGSIPU and many other Indian Universities. • The text material is self-explanatory and the language is vivid and lucid. • For each topic several solved examples, carefully selected to cover all aspects of the topic are covered. • Most of the questions conform to trend questions appearing in GGSIPU. Contents :- 1. Complex Number, 2. Sequence, 3. Infinite Series, 4. Vector Calculus, 5. Fourier Series, 6. Ordinary Differential Equations, 7. Linear Differential Equation of Higher Order and Special Methods. About the Author :- J. P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini, Delhi. He has more than 10 years of rich experience of teaching Real Analysis, Mathematical Statistics, Calculus, Numerical Methods and Discrete Mathematics to the students of MCA and BCA. He has taught at various affiliated Institutes of GGSIPU. His areas of interest include Mathematical Statistics, Number Theory, Theory of Computation, Numerical Methods, Discrete Mathematics and Real Analysis.

Fields and Galois Theory - John M. Howie

Author

John M. Howie

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181289834
YOP : 2008

Binding : Paperback
Total Pages : 240
CD : No

About the Book :- The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra. This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection. Topics covered include :- • rings and fields • integral domains and polynomials • field extensions and splitting fields • applications to geometry • finite fields • the Galois group • equations Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided. Contents :- Preface 1. Rings and Fields 2. Integral Domains; Polynomials 3. Field Extensions 4. Applications to Geometry 5. Splitting Fields 6. Finite Fields 7. The Galois Group 8. Equations and Groups 9. Some Group Theory 10. Groups and Equations 11. Regular Polygons 12. Solutions Bibliography List of Symbols Index.

Probability Essentials - Jean Jacod

Author

Jean Jacod
Philip Protter

Cover Price : Rs 595.00

Imprint : Springer
ISBN : 8181289827
YOP : 2008

Binding : Paperback
Total Pages : 264
CD : No

About the Book :- This introduction to Probability Theory can be used, at the beginning graduate level, for a one-semester course on Probability Theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as Finance Theory (Economics), Electrical Engineering, and Operations Research. The text covers the essentials in a directed and lean way with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it brings them from a starting knowledge of the subject to a knowledge of the basics of Martingale Theory. After learning Probability Theory from this text, the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference. The second edition contains some additions to the text and to the references and some parts are completely rewritten. Contents :- 1. Introduction 2. Axioms of Probability 3. Conditional Probability and Independence 4. Probabilities on a Finite or Countable Space 5. Random Variables on a Countable Space 6. Construction of a Probability Measure 7. Construction of a Probability Measure on R 8. Random Variables 9. Integration with Respect to a Probability Measure 10. Independent Random Variables 11. Probability Distributions on R 12. Probability Distributions on R 13. Characteristic Functions 14. Properties of Characteristic Functions 15. Sums of Independent Random Variables 16. Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) 17. Convergence of Random Variables 18. Weak Convergence 19. Weak Convergence and Characteristic Functions 20. The Laws of Large Numbers 21. The Central Limit Theorem 22. L2 and Hilbert Spaces 23. Conditional Expectation 24. Martingales 25. Supermartingales and Submartingales 26. Martingale Inequalities 27. Martingale Convergence Theorems 28. The Radon-Nikodym Theorem References Index.

Survival Analysis : A Self - Learning Text - David G. Kleinbaum

Author

David G. Kleinbaum
Mitchel Klein

Cover Price : Rs 895.00

Imprint : Springer
ISBN : 8184890082
YOP : 2008
Edition : 2008

Binding : Paperback
Total Pages : 608
CD : No

About the Book :- This greatly expanded second edition of Survival Analysis- A Self-learning Text provides a highly readable description of state-of-the-art methods of analysis of survival/event-history data. This text is suitable for researchers and statisticians working in the medical and other life sciences as well as statisticians in academia who teach introductory and second-level courses on survival analysis. The second edition continues to use the unique "lecture-book" format of the first (1996) edition with the addition of three new chapters on advanced topics: Chapter 7: Parametric Models Chapter 8: Recurrent events Chapter 9: Competing Risks. Also, the Computer Appendix has been revised to provide step-by-step instructions for using the computer packages STATA (Version 7.0), SAS (Version 8.2), and SPSS (version 11.5) to carry out the procedures presented in the main text. The original six chapters have been modified slightly • to expand and clarify aspects of survival analysis in response to suggestions by students, colleagues and reviewers, and • to add theoretical background, particularly regarding the formulation of the (partial) likelihood functions for proportional hazards, stratified, and extended Cox regression models Contents :- Introduction to Survival Analysis.- Kaplan-Meier Survival Curves and the Log-Rank Test.- The Cox Proportional Hazards Model and Its Characteristics.- Evaluating the Proportional Hazards Assumption.- The Stratified Cox Procedure.- Extension of the Cox Proportional Hazards Model for Time-Dependent Variables.- Parametric Survival Models.- Recurrent Events Survival Analysis.- Competing Risks Survival Analysis. About the Authors :- David Kleinbaum is Professor of Epidemiology at the Rollins School of Public Health at Emory University, Atlanta, Georgia. Dr. Kleinbaum is internationally known for innovative textbooks and teaching on epidemiological methods, multiple linear regression, logistic regression, and survival analysis. He has provided extensive worldwide short-course training in over 150 short courses on statistical and epidemiological methods. He is also the author of ActivEpi (2002), an interactive computer-based instructional text on fundamentals of epidemiology, which has been used in a variety of educational environments including distance learning. Mitchel Klein is Research Assistant Professor with a joint appointment in the Department of Environmental and Occupational Health (EOH) and the Department of Epidemiology, also at the Rollins School of Public Health at Emory University. Dr. Klein is also co-author with Dr. Kleinbaum of the second edition of Logistic Regression- A Self-Learning Text (2002). He has regularly taught epidemiologic methods courses at Emory to graduate students in public health and in clinical medicine. He is responsible for the epidemiologic methods training of physicians enrolled in Emory’s Master of Science in Clinical Research Program, and has collaborated with Dr. Kleinbaum both nationally and internationally in teaching several short courses on various topics in epidemiologic methods.

Applied Mathematics - Gerald Dennis Mahan

Author

Gerald Dennis Mahan

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 8184890075
YOP : 2008

Binding : Paperback
Total Pages : 376
CD : No

About the Book :- Applied Mathematics is a textbook for a two-semester graduate course in Mathematical Methods in Physics. Most universities give this course, which is often taught jointly with the Engineering or Mathematics Departments. General topics include: group theory, linear equations, matrices, series, functions of complex variables, conformal mapping, special functions, and partial differential equations. Each chapter has numerous homework problems. The section on transforms includes those on Fourier and Laplace, as well as the modern topic of wavelets. The chapters on partial differential equations include: Laplace's, Poisson's, Helmholtz, diffusion, and wave equations. Related topics such as transforms and orthogonal functions are also discussed in depth. The new topic of wavelet transforms is included. Contents :- 1. Determinants. 2. Matrices. 3. Group theory. 4. Complex Variables. 5. Series. 6. Conformal Mapping. 7. Markov Averaging 8. Fourier Transforms. 9. Equations of Physics. 10. One Dimension. 11. Two Dimensions. 12. Three Dimensions. 13. Odds and Ends. About the Author :- Geralad D. Mahan was born and raised in Portland, Oregon. His degrees in physics include a B.A. from Harvard in 1959 and a Ph.D. from the University of California, Berkeley, in 1964. He worked full-time at the General Electric Research and Development Center from 1964-1967, and continued part time and as a consultant until 1995. He had faculty appointments in physics at the University of Oregon (1967-1973), Indiana University (1973-1984), and the University of Tennessee (1984-2001). The latter appointment was held jointly with Oak Ridge National Laboratory. In 2001, he joined the faculty of Pennsylvania State University in University Park. He is a Fellow of the American Physical Society, and a member of the Materials Research Society, and a member of the U.S. National Academy of Sciences.

Mathematical Logic for Computer Science 2/E - Ben- Ari

Author

MORDECHAI BEN-ARI

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 9781447173618
YOP : 2017

Binding : Paperback
Total Pages : 318
CD : No

About the Book :- Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems. The logical systems presented are: - Propositional calculus (including binary decision diagrams); - Predicate calculus; - Resolution; - Hoare logic; - Z; - Temporal logic. Contents :- Preface.- Introduction.- Propositional Calculus: Formulas, Models, Tableaux.- Propositional Calculus: Deductive Systems.- Propositional Calculus: Resolution and BDDs.- Predicate Calculus: Formulas, Models, Tableau.- Predicate Calculus: Deductive Systems.- Predicate Calculus: Resolution.- Logic Programming.- Programs: Semantics and Verification.- Programs: Formal Specification with Z.- Temporal Logic: Formulas, Models, Tableaux.- Temporal Logic: Deduction and Applications.- Appendix: Set Theory; Further Reading; Bibliography; Index of Symbols; Index. About the Author :- Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He has published textbooks on concurrent programming and programming languages.

Complex Variables (Indian Reprint 2015) - Steven G Krantz

Author

Steven G Krantz

Cover Price : Rs 1,995.00

Imprint : T & F / Routledge
ISBN : 9781584885807
YOP : 2015

Binding : Hardback
Total Pages : 440
CD : No

About the Book :- From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice. The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, Maple™, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering. Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences. Contents :- Preface. Basic Ideas. Holomorphic and Harmonic Functions. The Cauchy Theory. Applications of the Cauchy Theory. Isolated Singularities. The Argument Principle. The Geometric Theory. Applications of Conformal Mapping. Harmonic Functions. Transform Theory. PDEs and Boundary Value Problems. Computer Packages. Appendices. Bibliography. Index.

Guide to Mathematical Modelling - Dilwyn Edards

Author

Dilwyn Edards
Mike Hamson

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan
ISBN : 0230574106
YOP : 2007
Edition : 2007

Binding : Paperback
Total Pages : 336
CD : No

About the Book :- A basic introduction to Mathematical Modelling, this book encourages the reader to participate in the investigation of a wide variety of modelling examples. These are carefully paced so that the readers can identify and develop the skills which are required for successful modelling. The examples also promote an appreciation of the enormous range of problems to which mathematical modelling skills can be usefully applied. Contents :- What is Modelling ? Getting Started Modelling Methodology Modelling Skills Using Difference Equations Using Differential Equations Using Random Numbers Using data Example Models Report Writing and Presentation About the Book :- DILWYN EDWARDS is Senior lecturer in Mathematics at the University of Greenwich MIKE HAMSON was formerly Senior Lecturer in Mathematics at the Glasgow Caledonian University.

Linear Algebra : A Pure Mathematical Approach - Harvey E. Rose

Author

Harvey E. Rose

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 8181282149
YOP : 2008

Binding : Paperback
Total Pages : 264
CD : No

About the Book :- Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach. A large number of examples, exercises and problems are provided. Answers and/or sketch solutions to all of the problems are given in an appendix. The intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a "second course" in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, the book can be used for a "first course" for more advanced students. Contents :- Preface Chapter 1 - Algebraic Preamble Chapter 2 - Vector Spaces and Linear Maps Chapter 3 - Matrices, Determinants and Linear Equations Chapter 4 - Cayley- Hamilton Theorem and Jordan Form Chapter 5 - Interlude on Finite Fields Finite Fields Chapter 6 - Hermitian and Inner Product Spaces Chapter 7 - Selected Topics Appendix A - Set theory Appendix B - Answers and Solutions to the problems Bibliography Index.

Basic Mathematics for Bca - J.P. Singh

Author

J.P. Singh

Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789380618685
YOP : 2011

Binding : Paperback
Total Pages : 392
CD : No

About the Book This book primarily aims at students preparing for BCA II Semester examination conducted by GGSIPU. This book covers the complete syllabus of BCA II Semester of GGSIPU. Salient features: 1. The text matter is self-explanatory and the language is vivid and lucid. 2. To simplify the process of conceptual assimilation, problems have been segregated as LOTS (Lower Order Thinking Skills) and HOTS (Higher Order Thinking Skills). 3. Most of the questions conform to the trend questions appearing in GGSIPU. Contents 1. Set Theory 2. Relations 3. Functions 4. Posets and Lattices 5. Limits and Continuity of Functions of Several Variables 6. Partial Differentiation 7. Multiple Integrals 8. Review of Two Dimensional 9. Solid Geometry About the Author J.P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has more than 12 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi. He is life time member of the Indian Mathematical Society. His areas of interest include Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation.

Business Mathematics & Statistics Reprint 2016 - B. M. Aggarwal

Author

B. M. Aggarwal

Cover Price : Rs 495.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9788180522857
YOP : 2015

Binding : Paperback
Size : 7.25
Total Pages : 800
CD : No

Salient Features of the Book :- • The book addresses concepts through detailed explanation and short illustrations. • Has a compilation of a large number of questions of different universities with solved examples. • Unsolved Questions at the end of each chapter for independent practice are a key feature of the text. • Very student friendly, it enables to analyse text with self evaluation tests in the form of Multiple Choice and Short Answer Questions. • Although the book has been made tailor specific for the B. Com IInd year of Delhi University, it can be used as a handy text for all the students preparing for other examinations with this syllabus. Contents :- Unit I: Business Mathematics 1. Matrices and Determinants 2. Applications of Matrices and Determinants to Business and Economics 3. Functions, Limits and Continuity 4. Differentiation 5. Applications of Integration to Business and Economics 6. Integral Calculus 7. Applications of Integrations to Business and Economics 8. Basic Mathematics of Finance Unit II: Business Statistics 1. Introduction to Statistics 2. Preparation of Frequency Distribution 3. Statistical Averages (Measures of Central Tendency) 4. Measures of Variation 5. Correlation and Regression Analysis 6. Index Numbers 7. Time Series About the Author :- B. M. Aggarwal graduated with Honors in Mathematics from Punjab University followed by a Masters degree in Mathematics from Meerut University and a degree in Electronics and Telecommunication Engineering from the Institute of Electronics and Telecommunications Engineering, Lodhi Road, New Delhi. A versatile teacher and a reputed Professor of Mathematics, Statistics and Operations Research the author has served in many reputed Management Institutes in Delhi and NCR. His presentation can be seen through his lucid and logical treatment of the text.

An Introduction to Wavelet Analysis - David F. Walnut

Author

David F. Walnut

Cover Price : Rs 995.00

Imprint : Springer
ISBN : 8184890204
YOP : 2008

Binding : Paperback
Total Pages : 472
CD : No

Review :- "D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!" — Bulletin of the AMS About the Book :- An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical prerequisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features :- * Rigorous proofs with consistent assumptions about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure). * Complete background material on is offered on Fourier analysis topics. * Wavelets are presented first on the continuous domain and later restricted to the discrete domain for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory, " provides a guide to current literature on the topic. * Over 170 exercises guide the reader through the text. An Introduction to Wavelet Analysis is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals. Contents :- Preface Part I: Preliminaries Functions and Convergence Fourier Series The Fourier Transform Signals and Systems Part II: The Haar System The Haar System The Discrete Haar Transform Part III: Orthonormal Wavelet Bases Mulitresolution Analysis The Discrete Wavelet Transform Smooth, Compactly Supported Wavelets Part IV: Other Wavelet Constructions Biorthogonal Wavelets Wavelet Packets Part V: Applications Image Compression Integral Operators Appendix A: Review of Advanced Calculus and Linear Algebra Appendix B: Excursions in Wavelet Theory Appendix C: References Cited in the Text Index.

Mathematics - 1 : FOR BCA - Zubair Khan

Author

Zubair Khan
Shadab Ahmad Khan
Qazi Shoeb Ahmad

Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 8180522946
YOP : 2009

Binding : Paperback
Total Pages : 600
CD : No

About the Book :- This book is designed to meet the requirements of I year rather I semester students of B.C.A. The book covers subject matter on complex numbers, trigonometry, matrices and determinants, differential calculus, integral calculus, vector calculus and their applications. Each unit of the book contains a variety of solved examples to explain the relevant concepts. Comprehensive exercises have been given at the end of each unit for practice and self assessment. This book is very useful for B.C.A. students of Integral University and the various other Universities. Salient features :- • The subject matter has been presented in a very simple language and lucid manner. • Step-wise treatment of difficult concepts makes them for easily understable. • Each chapter contains variety of illustrations to explain the relevant concepts. • Comprehensive exercises have been given at the end each chapter for practice. Contents :- Preface 1. Trigonometry and Complex Numbers 2. Matrices and Determinant 3. Differential Calculus 4. Integral Calculus 5. Vector Calculus About the Authors :- Dr. Zubair Khan is working as Lecturer in Department of Mathematics, Integral University, Lucknow. Dr. Khan has obtained his M.Sc., M.Phil. and Ph.D. degrees in Mathematics from Aligarh Muslim University, Aligarh. He has about four years of teaching experience at graduate and postgraduate levels. Dr. Khan has published a number of research papers in various National and International Journals of repute. The areas of his interest from research point of view are Applied Functional Analysis and Variational Inequalities. Shadab Ahmad Khan is working as Lecturer in Department of Mathematics, Integral University, Lucknow. Mr. Khan has done M.Sc. in Mathematics from Aligarh Muslim University, Aligarh. He has more than five years of teaching experience at graduate and post graduate levels. He has enrolled himself for Ph.D. degree in Lucknow University, selecting Differential Geometry as the research area. Dr. Qazi Shoeb Ahmad is working as Assistant Professor in Department of Mathematics, Integral University, Lucknow. Dr. Ahmad has obtained M.Sc. and Ph.D. degrees in Operations Research from Aligarh Muslim University, Aligarh. He has more than eight years of teaching experience at graduate and postgraduate levels. Dr. Ahmad has published a number of research papers in prestigious National and International Journals. His area of research interest includes Integer Programming, Sequencing and Mathematical Programming in Sampling.

VECTOR ANALYSIS AND CARTESIAN TENSORS 3RD ED, INDIAN REPRINT - D.E. BOURNE (EX)

Author

D.E. BOURNE
P.C. KENDALL

Cover Price : £ 5.99

Imprint : CRC Press
ISBN : 9780748754601
YOP : 2014

Binding : Paperback
Total Pages : 316
CD : No

This is a comprehensive self-contained text suitable for use by undergraduate mathematics, science and engineering students following courses in vector analysis. The earlier editions have been used extensively in the design and teaching of many undergraduate courses. Vectors are introduced in terms of Cartesian components, an approach which is found to appeal to many students because the basic algebraic rules of composition of vectors and the definitions of gradient divergence and curl are thus made particularly simple. The theory is complete, and intended to be as rigorous as possible at the level at which it is aimed. More advanced work on tensors is also included. For this edition, the book has been redesigned throughout, with alterations to the notation, and the inclusion of further material on applications, for example, on the existence and nature of angular velocity. There is also a brief introduction to the method of steepest descent. Dr Bourne and Professor kendall have collaborated over a period of 20 years and are well-known for their contributions to teaching and mathematics education. Their research, in topics ranging from the flow of molten glass to electromagnetic theory, has been carried out at the Universities of Sheffield, Alaska, Colorado, Keele and London. Contents Preface to second edition 1. Rectangular Cartesian coordinates and rotation of axes 2. Scalar and vector algebra 3. Vector functions of a real variable, Differential geometry of curves 4. Scalar and vector fields 5. Line, surface and volume integrals 6. Integral theorems 7. Applications in potential theory 8. Cartesian tensors 9. Representation theorems for isotropic tensor functions Appendix A Determinants Appendix B Expressions for grad, div, curl, and V2 in cylindrical and spherical polar coordinates Appendix C The chain rule for Jacobians Answers to exercises Index

Topology : A Geometric Approach - M. Ganesh

Author

M. Ganesh

Cover Price : Rs 180.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 8180522407
YOP : 2009

Binding : Paperback
Total Pages : 212
CD : No

About the Book :- Topology is a simultaneous generalization of two aspects: (1) the metric spaces (that includes normed linear spaces and inner product spaces and — both finite and infinite dimensional), and (2) the various geometries (Euclidean, affine, and projective). Almost all the books in the market are based on the first view point, ignoring or paying very little attention to the second view point. This book emphasizes more on the second point of view, without losing focus on the first point of view. Moreover, the author has taken great pain in presenting the subject matter in a cogent manner and with enough clarity, so that a student can do self-study. At the same time, rigor has not been sacrificed or diluted. This book is an outgrowth of the authors many years of experience in teaching topology at the postgraduate level and, therefore, intended especially for that level. Plenty of worked out examples and problems have been included to benefit both the teachers and the students. Plenty of figures are included as visual aids for enhancing the understanding. Certain topics, which are interesting but may prove to be a digression, have been dealt in appendices at the end of each chapter, giving adequate subjective information. On the whole, this book will be a welcome addition to the existing literature on topology and anticipates all success. About the Author :- Presently, M. Ganesh is a Professor of Mathematics at the Birla Institute of Technology & Science (BITS), Pilani (Rajasthan). The author received his Ph. D. degree from the University of Madras in the year 1979. Prof. Ganesh already has two books to his credit: the first one is entitled “Introduction to Fuzzy Sets & Fuzzy Logic”, published by Prentice Hall of India and the second is entitled “Basics of Computer Aided Geometric Design: An Algorithmic Approach”, published by I.K. International Publishers. The author has also published several papers in reputed National and International Journals. The areas of his current research interests include applications of fuzzy logic in decision making, computer science, and control theory. His other interests include theory of computability, cryptography and formal methods in program verifications.

Mathematics - II : FOR BCA - Shadab Ahmad Khan

Author

Shadab Ahmad Khan
Qazi Shoeb Ahmad
Zubair Khan

Cover Price : Rs 235.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 8180521702
YOP : 2009

Binding : Paperback
Total Pages : 384
CD : No

About the Book :- This book is designed to meet the requirements of I year, II semester students of B.C.A. The book covers the topics of Partial Differentiation, Ordinary Differential Equations, Partial Differential Equations, Geometry, Probability, Probability Distributions and Statistics. Each unit contains variety of solved examples to explain the relevant concepts. Comprehensive exercises have been given in each unit for practice. This book can be useful for B.C.A. students of Integral University and other Indian Universities. Salient features :- • The subject matter has been presented in a simple and lucid form. • Comprehensive step-by-step explanations for easier understanding. • Each chapter contains variety of illustrations to explain the relevant concepts. • Comprehensive exercises have been given at the end of each chapter for practice. Contents :- Preface, Unit-I : Partial Differentiation and its Applications, Unit-II : Ordinary Differential Equations, Unit-III : Partial Differential Equation and Geometry, Unit-IV : Probability and Distributions, Unit-V : Measures of Central Tendency. About the Authors :- Shadab Ahmad Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his B.Sc. and M.Sc. in Mathematics from Aligarh Muslim University, Aligarh. He has more than five years of teaching experience at graduate and postgraduate levels. He has enrolled himself as a research scholar in the field of Differential Geometry in Lucknow University. He has already four books to his credit. Dr. Qazi Shoeb Ahmad is working as Assistant Professor in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc. and Ph.D. in Operations Research from Aligarh Muslim University, Aligarh. He has more than eight years of teaching experience at graduate and postgraduate levels. Dr. Ahmad has published a number of research papers in prestigious national & international journals. His area of research interest includes Integer Programming, Sequencing and Mathematical Programming in Sampling. He has already four books to his credit. Dr. Zubair Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc., M.Phil. and Ph.D. in Mathematics from Aligarh Muslim University, Aligarh. He has about four years of teaching experience at graduate and postgraduate levels. Dr. Khan has published a number of research papers in prestigious national & international journals. His area of research interest is Applied Functional Analysis, Variational Inequalities. He has already one book to his credit.

Business Mathematics & Business Statistics - R.S. Soni and Avneet Kaur Soni

Author

R.S. Soni
Avneet Kaur Soni

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9788180521577
YOP : 2016

Binding : Paperback
Total Pages : 598
CD : No

New Arrival

About the Book :- This book is intended primarily for students preparing Paper VI for B.Com. Course (Part II) Examination conducted by the University of Delhi. The book has been written strictly in accordance with the latest syllabus prescribed by the University of Delhi and other Universities having similar syllabus. The text has grown from authors long teaching experience of over thirty-three years to the students of Commerce and Business Economics at different levels. Salient features of this book are: œ The book has simple and lucid language. œ Requires no previous knowledge of the subject. œ Each chapter starts with chapter outline and learning objectives. œ Difficult concepts have been explained in a simple and easy manner with examples. œ Written with a view to present a qualitative understanding of the subject. œ Contains large number of solved examples for better understanding of concepts. œ Unsolved problems for self-practice have been taken from recent examination papers of B.Com (Hons.) and B.Com (Pass). œ Answers to all the problems in the form of self-practice problems are given along with problems or at the end of self-practice problems. Contents Part A : 1. Matrices and Determinants 2. Applications of Matrices to Business and Economics 3. Functions, Limit and Continuity 4. Differentiation 5. Applications of Derivatives to Business and Economics 6. Integration 7. Applications of Integration to Business and Economics 8. Mathematics of Finance Part B : 1. Introduction to Statistics 2. Frequency Distribution 3. Measures of Central Tendency 4. Measures of Variation 5. Correlation Analysis 6. Regression Analysis 7. Index Numbers 8. Analysis of Time Series. About the Author Dr. R.S. Soni is a Associate Professor in the Department of Mathematics, Sri Guru Nanak Dev Khalsa College, Devnagar, University of Delhi, since 1976. Dr. Soni has a brilliant first class academic record. He obtained his Ph. D degree from the University of Delhi in 1975. Many of his research papers have been published in Indian and International journals of high repute. He has been teaching Mathematics and Statistics for over thirty-three years. Dr. Soni is the author of several mathematics textbooks.

Numerical and Statistical Techniques - Qazi Shoeb Ahmad

Author

Qazi Shoeb Ahmad
Zubair Khan
Shadab Ahmad Khan

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9788180522598
YOP : 2015

Binding : Paperback
Total Pages : 448
CD : No

New Arrival

About the Book :- The book is designed to meet the requirements of B.Tech, B.Tech (Biotech), B.C.A. students of Integral University and its study centers, Lucknow University, Jamia Hamdard and various other Universities. The book covers the topics of Error and Computer Arithmetic, Solution of Algebraic and Transcendental Equations, Solution of Simultaneous Equations, Finite Differences, Interpolation, Numerical Differentiation and Integration, Solution of Differential Equations, Curve Fitting, Regression Analysis, Time Series and Forecasting, Testing of Hypothesis. Each chapter contains variety of solved examples to explain the relevant concepts. Comprehensive exercises have been given in each chapter for practice. Salient features: ● The subject-matter has been presented in a simple and lucid form. ● Comprehensive step by step explanations for easier understanding. ● Each chapter contains variety of illustrations to explain the relevant concepts. ● Comprehensive exercises have been given at the end of each chapter for practice. Contents Preface 1. Error and Computer Arithmetic 2. Solution of Algebraic and Transcendental Equations 3. Finite Differences 4. Interpolation 5. Numerical Differentiation and Integration 6. Numerical Solution of Ordinary Differential Equations 7. Curve Fitting 8. Regression Analysis 9. Time Series and Forecasting 10. Test of Significance and Analysis of Variance Appendix, Index. About the Author Dr. Qazi Shoeb Ahmad is working as Assistant Professor in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc. and Ph.D. in Operations Research from Aligarh Muslim University, Aligarh. He has more than eight years of teaching experience at graduate and postgraduate levels. Dr. Ahmad has published a number of research papers in prestigious national and international journals. His area of research interest includes Integer Programming, Sequencing and Mathematical Programming in Sampling. The author already has five books in his credit. Dr. Zubair Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc., M.Phil and Ph.D. in Mathematics from Aligarh Muslim University, Aligarh. He has about five years of teaching experience at graduate and postgraduate levels. Dr. Khan has published a number of research papers in prestigious national and international journals. His area of research interest is Applied Functional Analysis, Variational Inequalities. He has also two books in his credit. Shadab Ahmad Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his B.Sc. and M.Sc. in Mathematics from Aligarh Muslim University, Aligarh. He has more than five years of teaching experience at graduate and postgraduate levels. He has enrolled himself as a research scholar in the field of Differential Geometry in Lucknow University. The author already has five books in his credit.

Classification of Lipschitz Mappings, Indian Reprint - Lukasz Piasecki (EX)

Author

Lukasz Piasecki

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781466595217
YOP : 2015

Binding : Hardback
Total Pages : 234
CD : No

Deep understanding of the properties of Lipschitzian mappings is important for all levels of study in many branches of mathematics. This book by Lukasz Piasecki is a good choice for achieving such an understanding in the framework of mappings in general metric spaces, in particular, Banach spaces. Moreover, it gives new insight into the theory of Lipschitzian mappings via a study of the mean Lipschitz condition. The book is written in a very clear and reader-friendly way. The author gives many examples illustrating various aspects of presented results.” —Stanislaw Prus, Marie Curie-Sklodowska University "… a self-contained, readable and precise course on the subject. Besides the presentation of the theory, the true value of the book lies in a collection of cleverly chosen interesting examples. “ —Kazimierz Goebel, Maria Curie-Sklodowska University "I strongly recommend this book for advanced undergraduate and graduate students … The reader will find a new classification of this kind of mapping as well as many examples and illustrations designed to help the reader understand the definitions, properties, and results…. I also recommend this book for analysts or mathematicians who are looking for new topics to research." —Victor Perez-Garcia, University of Veracruz Classification of Lipschitz Mappings presents a systematic, self-contained treatment of a new, more precise classification of Lipschitz mappings and its application in many topics of metric fixed point theory. The mean Lipschitz condition introduced by Goebel, Japon Pineda, and Sims is relatively easy to check and turns out to satisfy several principles: regulating the possible growth of the sequence of Lipschtz constants k(Tn), Ensuring good estimates for k0(T) and k8(T) and Providing some new results in metric fixed point theory. Contents Introduction The Lipschitz Condition Nonlinear spectral radius Uniformly lipschitzian mappings Basic Facts on Banach Spaces Convexity The operator norm Dual spaces, reexivity, the weak, and weak* topologies Mean Lipschitz Condition Nonexpansive and mean nonexpansive mappings in Banach spaces General case On the Lipschitz Constants for Iterates of Mean Lipschitzian Mappings A bound for Lipschitz constants of iterates A bound for the constant k∞(T) Moving averages in Banach spaces A bound for the constant k0(T) More about k(Tn), k0(T), and k∞(T) Subclasses Determined by p-Averages Basic definitions and observations A bound for k(Tn), k∞(T), and k0(T) On the moving p-averages Mean Contractions Classical Banach’s contractions On characterizations of contractions On the rate of convergence of iterates Nonexpansive Mappings in Banach Space The asymptotic center technique Minimal invariant sets and normal structure Uniformly nonsquare, uniformly noncreasy, and reflexive Banach spaces Remarks on the stability of f.p.p. The case of ℓ1 Mean Nonexpansive Mappings Some new results of stability type Sequential approximation of fixed points The case of n = 3 On the structure of the fixed points set Mean Lipschitzian Mappings with k > 1 Losing compactness in Brouwer’s Fixed Point Theorem Retracting onto balls in Banach spaces Minimal displacement Optimal retractions Generalized characteristics of minimal displacement Bibliography Index

Elements of Graph Theory - S.K. Yadav

Author

S.K. Yadav

Cover Price : Rs 270.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9380618487
YOP : 2010

Binding : Paperback
Total Pages : 273
CD : No

About the Book This book is designed to meet the syllabus requirement of the students of B.Tech., M.Tech. (C.S.), M.Sc. (Mathematics), M.Sc. (C.S.), M.Sc. (Electronics), M.C.A., and other professional courses of various national and international universities. The questions asked in various universities and professional courses have also been added. The students of open and distance education courses will find the book very helpful. Contents 1. The basics of Graph Theory 2. Trees 3. Planar Graphs 4. Directed Graphs 5. Matching and Covering 6. Colouring of Graphs 7. Ramsey Theory for Graphs 8. Emerging Trends in Graph Theory. References, Index About the Author Prof. Santosh Kumar Yadav has been associated with academic and research activities for two decades. He did his Masters in Science (Physics, Mathematics, Applied Mathematics and Mathematics with Computer Applications), M.Phil (Mathematics, Computer Science) Ph.D, M.Tech (C.S.E.),M.B.A (Education Management). Prof. Yadav has Written more than a dozen text and reference books and edited more than a hundred self-learning materials for different Universities. He is the editor for four reputed international journals of research and has supervised more than 70 research scholars.

Complex Analysis - Anuradha Gupta

Author

Anuradha Gupta

Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789381162248
YOP : 2011

Binding : Paperback
Total Pages : 432
CD : No

About the Book The textbook is a continuation of the study of Calculus, but as the study of functions of complex variables. The first goal in writing this book is to present the theory of analytic functions in a more accessible way in the early stages of his/her complex analysis study. The second aim of this book is to give the students wide applications of complex variable techniques as complex analysis is a powerful tool in applied mathematics. The third aim of this book is to provide a comparative study between real variables and complex variables of various topics. Basically those areas where real and complex calculus differ, have been discussed to give the clarity about the concept. I have also provided lots of examples and have tried very hard to supply all pertinent detail of their solution. The corresponding exercise sets are divided in order to make the study easier. A multifaceted book written to keep the interest of B.Sc (Hons) Mathematics (Part III), M.Sc.(Mathematics-Part I) students of University of Delhi. This book is also useful for those who want to appear in their National eligibility Test for Lecturership in Mathematics. Contents 1. Complex Number and The Complex Plane 2. Functions of Complex Variable 3. Analytic Functions 4. Elementary Functions 5. Complex Integration 6. Cauchys Integral Formulas and their Consequences 7. Analytic Functions in a Disc 8. Simply Connected Region 9. Isolated Singularities 10. The Calculus of Residues 11. Contour Integration and Summation of Series 12. Conformal Mapings 13. Schwarzs Lemma-An Automorphism of Disc, Appendix, Bibliography, Index About the Author Dr. Anuradha Gupta, a PhD from University of Delhi, is an Associate Professor in the Department of Mathematics, Delhi College of Arts and Commerce (University of Delhi). She has more than 20 years of rich experience of teaching Real Analysis, Algebra, Complex Analysis and Discrete Mathematics to the students of undergraduate and postgraduate levels of University of Delhi. Her major areas of interest include Operator theory, Functional Analysis, Calculus, Complex and Real Analysis. There are ten research papers published in national and international journals to her credit. She has also written a book entitled Business Mathematics.

Applied Mathematics - II, - Singh Abhimanyu

Author

Abhimanyu Singh

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789381162798
YOP : 2015

Binding : Paperback
Total Pages : 654
CD : No

About the Book This book covers the complete syllabi of the paper Applied Mathematics-II of second semester of B.Tech. course of GGSIP University, Delhi, and first & second semesters of other national and international Engineering and Technological Institutions. The matter is presented in so simple manner that even an average student can have a good command on this difficult subject. The text is equipped with a large number of solved problems with enough unsolved exercises. I hope the book will serve its purpose. Contents Unit I: Calculus of Several Variables 1. Partial Differentiation 2. Applications of Partial Differentiation 3. Multiple Integrals Unit II: Functions of A Complex Variable 4. Functions of a Complex Variable 5. Conformal Transformation 6. Complex Integration 7. Power Series Unit III: Vector Calculus 8. Vector Differentiation 9. Vector Integration Unit IV: Laplace Transform 10. Laplace Transformation 11. Inverse Laplace Transforms About the Author Abhimanyu Singh is currently working as an Assistant Professor in the Dept of Mathematics, GGSIPU (affiliated institute,)Delhi. He has more than 15 years of experience in teaching Engineering Mathematics to B.E.and B.Tech. students at Delhi Technological University (formerly Delhi College of Engineering) and Guru Gobind Singh Indraprastha University, Delhi.

Discrete Mathematics with Graph Theory - S.K. Yadav

Author

S.K. Yadav

Cover Price : Rs 495.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127185
YOP : 2016

Binding : Paperback
Size : 5.50" X 8.50"
Total Pages : 670
CD : No

About the Book This book has been designed to meet the syllabus requirements of the students of B.Sc.(H)(Math/Computer Sc./Physical Sc.), B.C.A/M.C.A., B.Tech. (C.S.E., E.C.E., I.T.,), M.Tech.(C.S.E./I.T.), M.Sc. (Mathematics/C.S./Electronics) and other professional courses of various Universities/ Institutions at home and abroad. The students of Open and Distance Education courses will find the book most useful. Contents 1. The Language of Sets 2. Basic Combinatorics 3. Mathematical Logic 4. Relations 5. Functions 6. Lattice Theory 7. Boolean Algebras and Applications 8. Fuzzy Algebra 9. Formal Languages and Automata Theory 10. The Basics of Graph Theory 11. Trees 12. Planar Graphs 13. Directed Graphs 14. Matching and Covering 15. Colouring of Graphs, References, Index About the Author Dr.Santosh Kumar Yadav (b-1968)has been associated with academic and research activities for more than two decades. He has been an active and dynamic administrator as Director (Academics and Research)at J.J.T. University, Rajasthan. As an academician he has taught undergraduates and postgraduate students in different premier institutions including various colleges of University of Delhi in different capacities. As a researcher, Dr. Yadav has guided more than 70 research scholars of different universities at home and abroad. As an author he has written more than a dozen books and more than a hundred self-learning materials of different universities. Dr. Yadav is editor of six well reputed International Journals of Research and Life Member of 24 reputed professional apex bodies of academics and research.

DU B.SC (HONS),MATH, SEM-III: MULTIVARIABLE CALCULUS - ANURADHA GUPTA

Author

ANURADHA GUPTA

Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127222
YOP : 2016

Binding : Paperback
Total Pages : 326
CD : No

About the Book Multivariable calculus is the extension of calculus in one variable to calculus in more than one variable where the differentiated and integrated functions involve multivariables rather than just one. This book is written to fulfill the needs of B.Sc. (Maths) IIIrd semester students of University of Delhi so that the students learn the concepts of calculus for the function of several variables thoroughly and apply them in new and novel ways. The theme of the book is that the Calculus is about logical thinking one cannot memorize all. The examples and exercises of the book are meticulously crafted and honed to meet the needs of the students who are keen to know about multivariable calculus. Starting from the basics of vector calculus and covering upto double and triple integrals the book provides the students a deep study of the calculus of functions of more than one variables. The book Multivariable Calculus combines in depth the theory with examples and applications of the concepts related to the functions of several variables. Contents 1. Functions and Graphs 2. Vectors and Geometry of Euclidean Space 3. Vector-Valued Functions 4. Partial Differentiation 5. Multiple Integrals 6. Vector Fields, Solutions, Table, Bibliography, Index About the Author Dr. Anuradha Gupta is an Associate Professor in the Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi. She has rich teaching experience of more than 21 years. She is actively involved in the research activities in the field of Operator Theory and Functional Analysis. Her research articles have been published in various national and international journals. She has also presented her research papers in several international conferences in India and abroad. She has also written two books “Business Mathematics” and “Complex Analysis” for the undergraduate students of various Universities in India.

B.Com (Hons),Sem-3: Business Mathematics - R.S. Soni

Author

R.S. Soni
Avneet Kaur Soni

Cover Price : Rs 450.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127246
YOP : 2016

Binding : Paperback
Total Pages : 698
CD : No

About the Book This book is intended primarily for students preparing Paper CH 3.1 for B.Com.(Hons.) Course, Semester-III, Examination conducted by the University of Delhi. The book has been written strictly in accordance with the latest syllabus prescribed by the University of Delhi and other Universities having similar syllabus. The text has grown from authors long teaching experience of over thirty-three years to the students of Commerce and Business Economics at different levels. Salient features of this book are: • The book has simple and lucid language. • Requires no previous knowledge of the subject. • Each chapter starts with chapter outline and learning objectives. • Difficult concepts have been explained in a simple and easy manner with examples. • Written with a view to present a qualitative understanding of the subject. • Contains large number of solved examples for better understanding of concepts. • Unsolved problems for self-practice have been taken from recent examination papers of B.Com (Hons.) and B.Com (Pass). • Answers to all the problems in the form of self-practice problems are given along with problems or at the end of self-practice problems. Contents 1. Matrices and Determinants 2. Applications of Matrices to Business and Economics 3. Functions, Limit and Continuity 4. Differentiation 5. Applications of Derivatives to Business and Economics 6. Partial Differentiation 7. Applications of Partial Differentiation to Business and Economics 8. Integration 9. Applications of Integration to Business and Economics 10. Mathematics of Finance 11. Mathematics of Finance-II 12. Linear Programming-I 13. Linear Programming-II (Simplex Method) About the Authors Dr. R.S. Soni is an Associate Professor in the Department of Mathematics, Sri Guru Nanak Dev Khalsa College, Devnagar, University of Delhi, since 1976. Dr. Soni has a brilliant first class academic record. He obtained his Ph.D. degree from the University of Delhi in 1975. Many of his research papers have been published in Indian and International journals of high repute. He has been teaching Mathematics and Statistics for over thirty-three years. Dr. Soni is the author of several mathematics textbooks. Avneet Kaur Soni has obtained B.Com (Hons.) degree from Delhi University, M.Com. degree from IGNOU and BCA degree from DOEACC 'A' Level. At present, she is pursuing Ph.D.

B.Sc(Hons), Math, Sem-III: Numerical Methods and Programming - Ranjna Mehta

Author

Ranjna Mehta
Seema Paliwal

Cover Price : Rs 175.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789382127192
YOP : 2016

Binding : Paperback
Total Pages : 182
CD : No

About the Book This book is useful for various graduate and postgraduate courses in Mathematics, Physics, Computer Science. The book covers the syllabus for B.SC (Hons.) Mathematics IInd year (IIIrd Semester) for the paper entitled III. 2, Numerical Method and Programming. This text has a student friendly approach with an easy to read writing style and a perfect blend of theory and numerical. It presents all the basis material in one place and gives an opportunity to understanding the topic in the most easy and comfortable way. A large number of examples are used to explain the concepts. The book contains number of exercises to help build confidence in students. Contents 1. Algorithm and Convergence, 2. Finite Differences and Interpolations, 3. Interpolation and Approximation, 4. Polynomial and Transcendental Equations, 5. System of Linear Algebraic Equations, 6. Numerical Differentiation and Numerical Integration, 7. Numerical Rule, 8. C++ Programming, Practice Problems, Reference, Question Paper About the Author Ranjna Mehta is an Associate Professor in the Department of Mathematics at Sri Venkateswara College. She did her Ph.D from University of Delhi in 1982. Four of her research papers have been published in Indian and Foreign journals Seema Paliwal is an Assistant Professor in the Department of Mathematics at Hindu College. She has over 12 years of teaching experience at the undergraduate level. Her area of interest are Numerical Analysis, Calculus, Analysis (Real & Complex), and Operator Theory.

Discrete Mathematics for Undergraduates , Revised & Updated - J.P. Singh

Author

J.P. Singh

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789381162910
YOP : 2018

Binding : Paperback
Total Pages : 340
CD : No

About the Book This book has been written for undergraduate students pursuing Discrete Mathematics as their subject. The book primarily aims at students preparing for BCA, Semester II examination conducted by GGSIP University. This book consists of eight chapters. All the chapters have been supplied by numerous solved examples and exercises along with their answers. The main objective of this book is to provide useful self-study material for the students. Clear diagrams have been drawn, text headings have been specified that helps students to grasp this subject easily. This will not only enhance students' understanding of the concepts discussed but will also prepare them for the examination. Salient features: 1. The text matter is self-explanatory and the language is vivid and lucid. 2. To simplify the process of conceptual assimilation, problems have been segregated as LOTS (Lower Order Thinking Skills) and HOTS (Higher Order Thinking Skills). 3. Most of the questions conform to the trend questions appearing in GGSIPU. 4. Clear diagrams are provided in support of text. 5. Symbols with their meanings are provided for the help of students. Contents 1. Set Theory 2. Relations 3. Functions 4. Posets and Lattices 5. Mathematical Logic 6. Graph Theory 7. Paths and Circuits 8. Graph Coloring About the Author J.P. Singh is a Professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini (Affiliated to GGSIP University), Delhi. He has more than 13 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi. He is a lifetime member of the Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Stochastic Process, Discrete Mathematics, Mathematical Statistics, Numerical Methods, Number Theory and Theory of Computation.

MODERN ADVANCED MATHEMATICS FOR ENGINEERS, WILEY INDIA , INDIAN REPRINT - VLADIMIR V. MITIN (EX)

Author

VLADIMIR V. MITIN
DMITRI A. RAMANOV
MICHAEL P. POLIS

Cover Price : Rs 3,995.00

Imprint : Wiley India
ISBN : 9788126539185
YOP : 2013

Binding : Hardback
Total Pages : 326
CD : No

Almost every discipline in electrical and computer engineering relies heavily on advanced mathematics. Modern Advanced Mathematics for Engineers builds a strong foundation in modern applied mathematics for engineering students, and offers them a concise and comprehensive treatment that summarizes and unifies their mathematical knowledge using a system focused on basic concepts rather than exhaustive theorems and proofs. The authors provide several levels of explanation and exercises involving increasing degrees of mathematical difficulty to recall and develop basic topics such as calculus, determinants, Gaussian elimination, differential equations, and functions of a complex variable. They include an assortment of examples ranging from simple illustrations to highly involved problems as well as a number of applications that demonstrate the concepts and methods discussed throughout the book. This broad treatment also offers • Key mathematical tools needed by engineers working in communications, semiconductor device simulation, and control theory • Concise coverage of fundamental concepts such as sets, mappings, and linearity • Thorough discussion of topics such as distance, inner product, and orthogonality • Essentials of operator equations, theory of approximations, transform methods, and • partial differential equations • A treatment that is adaptable for use with computer systems Modern Advanced Mathematics for Engineers gives students a strong foundation in modern applied mathematics and the confidence to apply it across diverse engineering disciplines. It makes an excellent companion to less general engineering texts and a useful reference for practitioners. Contents Dedication. Preface. The Basic of Set Theory. Relations and Mappings. Mathematical Logic. Algebraic Structures: Group Through Linear Space. Linear Mappings and Matrices. Metrics and Topological Properties. Banach and Hilbert Spaces. Orthonormal Bases and Fourier Series. Operator Equations. Fourier and Laplace Transforms. Partial Differential Equations. Topic Index. VLADIMIR V. MITIN and DMITRI A. ROMANOV are both Professors in the Department of Electrical and Computer Engineering at Wayne State University. MICHAEL P. POLIS is Professor in the School of Engineering and Computer Science at Oakland University in Michigan.

PARTIAL DIFFERENTIAL EQUATIONS AND THE FINITE ELEMENT METHOD, INDIAN REPRINT - PAVEL SOLIN (EX)

Author

PAVEL SOLIN

Cover Price : Rs 3,995.00

Imprint : Wiley India
ISBN : 9788126537570
YOP : 2013

Binding : Hardback
Total Pages : 490
CD : No

Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM. A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM. Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science. Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists. Contents List of Figures. List of Tables. Preface. Acknowldegments. 1. Partial Differential Equations. 2. Continuous Elements for 1D Problems. 3. General Concept of Nodal Elements. 4. Continuous Finite Elements for 2D Problems. 5. Transient Problems and ODE Solvers. 6. Beam and Plate Bending Problems. 7. Equations of Electrimagnetics. Appendix A: Basics of Functional Analysis. Appendix B: Software and Examples. References. Index. PAVEL SOLÍN, PhD, is Associate Professor in the Department of Mathematical Sciences at The University of Texas at El Paso. Prior to this appointment, Dr. Solin was a postdoctoral research associate at the Johannes Kepler University (Linz, Austria), The University of Texas at Austin, and Rice University (Houston, Texas). He received his PhD from the Charles University in Prague, Czech Republic, in 1999. Dr. Sol?n is a coauthor of the monograph Higher-Order Finite Element Methods.

Applied Mathematics -1 - Abhimanyu Singh

Author

Abhimanyu Singh

Cover Price : Rs 325.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789380156323
YOP : 2010

Binding : Paperback
Total Pages : 518
CD : No

About the Book This book is written to completely fulfil the requirement of first semester students of B. Tech. of GGSIPU, Delhi; and to partially fulfil the requirement of first semester students of Delhi Technological University, Delhi; Jamia Miliya Islamiya University, Delhi, and other Indian and Foreign Engineering and Technological Institutions. Contents Preface Syllabus 1. Complex Numbers 2. Infinite Series 3. Successive Differentiation 4. Expansion of Functions and Approximate Calculations 5. Asymptotes 6. Curvature 7. Curve Tracing 8. Integration 9. Area of Plane Curves (Quadrature) 10.Rectification 11.Volume and Surface of Solids of Revolutions 12.Matrices 13.Differential Equations About the Author Abhimanyu Singh has more than 13 years of teaching experience Engineering Mathematics to B.E. and B.Tech. Students at Delhi Technological University (formerly Delhi College of Engineering) and Guru Gobind Singh Indraprastha University, Delhi.

ENGINEERING MATHEMATICS - I - ABHIMANYU SINGH

Author

ABHIMANYU SINGH

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789381162392
YOP : 2012

Binding : Paperback
Total Pages : 584
CD : No

About the Book This book covers a wide range of first and second semester syllabus in mathematics of various Indian Technological Universities and International Engineering and Technological Institutions. This book will provide a foundation in mathematical principles, which will enable students to solve mathematical, scientific and engineering problems. The text, has been presented in a simple and lucid manner, includes a large number of solved and unsolved problems. Contents UNIT-I: DIFFERENTIAL CALCULUS-I 1. Successive Differentiation 2. Expansion of Functions and Approximate Calculations 3. Asymptotes 4. Curve Tracing 5. Partial Differentiation UNIT-II : DIFFERENTIAL CALCULUS–II 6. Jacobians 7. Approximate Calculations of One and Two Variable Functions 8. Maxima/Minima UNIT-III : MATRICES 9. Matrices UNIT-IV : MULTIPLE INTEGRALS 10.Double and Triple Integrals 11.Beta and Gama Functions, Dirichlet Integrals and Applications UNIT-V : VECTOR CALCULUS 12.Vector Calculus 13.Integration of Vector Functions Examination Paper 2007–11 About the Author Abhimanyu Singh is currently working as an Assistant Professor in the Department of Mathematics, GGSIPU (affiliated institute), Delhi. He has more than 15 years of experience in teaching Engineering Mathematics to B.E. and B.Tech. students at Delhi Technological University (formerly Delhi College of Engineering) and Guru Gobind Singh Indraprastha University, Delhi.

MATHEMATICAL ANALYSIS, INDIAN REPRINT - BERND S.W. SCHRODER (EX)

Author

BERND S.W. SCHRODER

Cover Price : Rs 3,495.00

Imprint : Wiley
ISBN : 9788126542376
YOP : 2013

Binding : Hardback
Total Pages : 578
CD : No

Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: Part One- presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. Part Two- explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. Part Three- provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics. Contents Preface. PART I. ANALYSIS OF FUNCTIONS OF A SINGLE REAL VARIABLE. 1. The Real Numbers. 2. Sequences of Real Numbers. 3. Continuous Functions. 4. Differentiable Functions. 5. The Riemann Integral I. 6. Series of Real Numbers I. 7. Some Set Theory. 8. The Riemann Integral II. 9. The Lebesgue Integral. 10.Series of Real Numbers II. 11.Sequences of Functions. 12.Transcendental Functions. 13.Numerical Methods PART II. ANALYSIS IN ABSTRACT SPACES. 14.Integration on Measure Spaces. 15.The Abstract Venues for Analysis. 16.The Topology of Metric Spaces. 17.Differentiation in Normed Spaces. 18.Measure, Topology and Differentiation. 19.Introduction to Differential Geometry 20.Hilbert Spaces. PART III. APPLIED ANALYSIS. 21.Physics Background. 22.Ordinary Differential Equations. 23.The Finite Element Method. Conclusion and Outlook. APPENDICES. A.Logic. A.1 Statements. A.2 Negations. B.Set Theory. B.1 The Zermelo-Fraenkel Axioms. B.2 Relations and Functions. C.Natural Numbers, Integers and Rational Numbers. C.1 The Natural Numbers. C.2 The Integers. C.3 The Rational Numbers. Bibliography. Index. Bernd S.W. Schroder, PhD, is Edmondson/Crump Professor in the Program of Mathematics and Statistics at Louisiana Tech University. Dr. Schröder is the author of over thirty refereed journal articles on subjects such as ordered sets, probability theory, graph theory, harmonic analysis, computer science, and education. He earned his PhD in mathematics from Kansas State University in 1992.

Operations Research (Revised and Updated Edition) - J.P. Singh

Author

J.P. Singh
N.P. Singh

Cover Price : Rs 550.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789380618128
YOP : 2017

Binding : Paperback
Size : 6.25
Total Pages : 562
CD : No

About the Book This book is written for courses like MBA, PGDM, M. Corn., MCA, BCA, B. Tech. BBA, BBA (CAM) and B. Sc. (Computers) for courses taught under titles as Management Science, Quantitative Methods, Introduction to Operations Research, Quantitative Techniques for Management, Quantitative Aids to Decision Making in GGSIPU, UPTU, MDU and other Indian Universities and B-Schools. Contents 1. Introduction, 2. Linear Programming: Formulation, 3. Linear Programming; The Graphical Method, 4. Linear Programming: The Simplex Method, 5. Duality and Sensitivity Analysis, 6. Transportation Problem, 7. Assignment Problem, 8. Decision Theory, 9. Game Theory, 10. Project Management: CPM and PERT, 11. Queuing Theory, 12. Replacement Models, 13. Sequencing Problem About the Authors JP Singh is a Professor in the Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has over 15 years of teaching experience in Operations Research, Discrete Mathematics, Numerical Methods, Mathematical Statistics and Calculus. He has taught at various affiliated institutes of GGSIPU. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a certified Six Sigma Green belt from Indian Statistical Institute, Delhi. He is a lifetime member of the Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Operations Research, Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation. NP Singh is a faculty in the Department of Management at Guru Nanak Institute of Management (GNIM), Delhi. He was awarded Gold Medal for securing top position in PGDM (Finance). He earned his M. Phil. (Finance) from University of Delhi. He has over 11 years of teaching experience in Operations Research, Business Statistics, Financial Management, Security Analysis and Portfolio management, International Financial Management and Derivatives and Risk Management. Teaching and research has been his core interests. He is also heading Centre for Research in Finance (CRIF) at GNIM. His research areas include Commodity and Financial Derivatives, Financial Modeling, Security Analysis and applications of Optimization Techniques in Finance. Some of his research papers have been published in journals of national repute. He has participated in research projects/CEP/workshops on topics like optimization methods, quantitative finance, financial modeling and risk management at institutes like IIM Calcutta, IIT Delhi and IIT Kharagpur.

Introduction to Matrix Theory - Arindama Singh

Author

Arindama Singh

Cover Price : Rs 995.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789386761200
YOP : 2018

Binding : Hardback
Size : 6.25" X 9.50"
Total Pages : 212
CD : No

About the Book Keeping the modest goal as a text book on matrix theory the approach here is straight forward and quite elementary. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schur triangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least squares solutions_ It includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts; and problems have been added at the end of each chapter. Most of these problems are theoretical in nature and they do not fit into the running text linearly. Exercises and problems form an integral part of the book. Contents 1. Matrix Operations 2. Systems of Linear Equations 3. Subspace and Dimension 4. Orthogonality 5. Eigenvalues and Eigenvectors 6. Canonical Forms 7. Norms of Matrices, Short Bibliography, Index. About the Author Dr. Arindama Singh is currently Professor at the Department of Mathematics, IIT Madras. He has 27 years of teaching and research experience out of which last 22 years is at IIT Madras. He has guided 5 Ph.D, 4 M.Phil and 18 M.Sc. students so far. He has published 3 books, 36 articles in refereed Journals and 10 papers in refereed conference proceedings. His areas of interest and research are Logic, Theory of Computation and LinearAlgebra.

Mathematics for Chemistry - Quddus Khan

Author

Quddus Khan

Cover Price : Rs 1,995.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789386761712
YOP : 2018

Binding : Hardback
Size : 6.25" X 9.50"
Total Pages : 468
CD : No

About the Book This textbook, Mathematics for Chemistry is written in accordance with the UGC model syllabus for the postgraduate students of chemistry of all Indian universities. It will also be useful for competitive examinations like IAS, PCS etc. The text starts with a chapter on preliminaries detailing the basic concepts and the results thereof that will be referred throughout the book. This is followed by an in-depth study of matrix algebra, vector algebra, calculus (differential and integral), differential equations, permutation and combination, and theory of probability. Some of the key features are: • Basics concepts presented in an easy-to-understand style. • Includes a large number of solved examples • Notes and remarks given at appropriate places. • Clean and clear illustrations/figures for better understanding • Exercise questions at the end of each Chapter Contents 1. Preliminaries 2. Matrix Algebra 3. Vector Algebra 4. Differential Calculus 5. Integral Calculus 6. Elementary Differential Equations 7. Permutation and Combination 8. Theory of Probability, Bibliography, Index About the Author Dr. Quddus Khan is Associate Professor in the Department of Applied Science and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi. He has been teaching UG & PG classes for the last eighteen years. He had also taught in Shibli National R G. College, Azamgarh (U.P.). He had also worked as a Young Scientist (PDF) in the Department of Mathematics, Faculty of Natural Science, Jamia Millia Islamia, New Delhi. Dr. Khan has to his credit 20 research papers on differentiable manifolds published in various national and international journals, five books on D.G. of manifolds, D.G. and its Application, Tensor analysis and its Application, Fundamental Concepts of recurrent manifold and Sasakian manifold and fundamental concept of symmetric manifold and Sasakian manifold and has also supervised two PhDs.

Essentials of Business Statistics - B.M.Aggarwal

Author

B.M. Aggarwal

Cover Price : Rs 495.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789381162736
YOP : 2014

Binding : Paperback
Total Pages : 800
CD : No

About the Book The book has been designed specifically to meet the requirements of all the students pursuing undergraduate studies in commerce. The book will serve equally well for the undergraduate management courses like BBA, BBE, etc. Salient features: 1. The treatment of the subject is conceptual and easily graspable even by average students. 2. A large variety of questions as solved examples have been selected from the question papers of equivalent examinations of different universities to apprise the students about the varying trends. 3. A large number of unsolved questions have been given at the end of each chapter for practice. 4. Numerous MCQs have been given at the end of each chapter for better conceptual understanding of the subject. 5. Keeping in view the wide applications, special emphasis has been given in detailed explanation of concepts and in normal distribution with separate tables. 6. Some unique features and their details have been added in rank correlation. Contents 1. Statistical Averages (Measures of Central Tendency) 2. Measures of Variation 3. Moments, Skewness and Kurtosis 4. Probability and Mathematical Expectation 5. Probability Distribution (Theoretical Distribution) 6. Decision Theory 7. Correlation and Regression Analysis Correlation 8. Index Numbers 9. Time Series About the Author B.M. Aggarwal, B.Sc. (Hons.) from Punjab University, later graduated from the Institute of Electronics and Telecommunication Engineers, New Delhi. He did his M.Sc (Mathematics) from Merrut University. In addition, he passed certificate courses in Microwave and Satellite Engineering from ALT Centre,Ghaziabad. The author is a visiting professor in quantitative techniques, operations research and research methods in various premier Institutes like IMT Ghaziabad, ICFAI Gurgaon, Asia Pacific Institutes of Management, Delhi besides several other Institutes. He has been in the field of books, from 1986 onwards, and has many books to his credit.

Calculus of Variations, Applications and Computations - C. Bandle (EX)

Author

C Bandle
J Bemelmans
M Chipot
J Paulin

Cover Price : Rs 4,995.00

Imprint : CRC / Lewis
ISBN : 9780582239623
YOP : 2014

Binding : Hardback
Total Pages : 294
CD : No

ABOUT THIS VOLUME This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of various areas of science and have experienced tremendous development during the last decades. Readership: This book should interest not only experts in partial differential equations but also graduate students, applied mathematics and computer users. PITMAN RESEARCH NOTES IN MATHEMATICS SERIES The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline. The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by Mathematical Review. This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph. Will also be considered for a place in the series. Normally homograph, material is required, even if written by more than one author, thus multi-author works will be included provided that there is a strong linking theme or editorial pattern. Contents Preface Isoperimetric Inequalities for a Generalized Multidimensional Muskat Problem Solution of a Free Boundary Problem of the Hele-Shaw Type, in the Ovsjannikov Scales Continuous Polarization and Symmetry of Solutions of Variational Problems with Potentials An Optimal Control Problem for a Nonlinear Elliptic Equation Arising from Population Dynamics Global existence of Functional Solutions for the Vlasov-Poisson-Fokker-Planck System in 3 D with Bounded Measures as Initial Data Numerical Methods for a Forward Backward Heat Equation On a Dirichlet Problem Related to the Invertibility of Mappings Arising in 2D Grid Generation On Rank One Convex Functions Which are Homogeneous of Degree One On the Approximation of the Curve Shortening Flow Flows Through Saturated Mass Exchanging Porous Media Under High Pressure Gradients Existence of Nontrivial Solutions to the Marguerre-Von Karman Equations, Quasiconvex Envelopes of Stored Energy Densities that are Convex with Respect to the Strain Tensor Application of Quasi Steady Solutions of Soil Freezing for Geotechnical Engineering Curvature Driven Interface Motion Discretization of Second Order Elliptic Differential Equations on Sparse Grids Hydrodynamic stability and a Posterior Error Control in the Solution of the Navier-Stokes Equations Partial Regularity for Incompressible Materials with Approximation Methods A Note About Relaxation of Vectorial Variational Problems Numerical Simulation of Boundary Layer Problem with Separation Maximal Inequalities and Applications to Regularity Problems in the Calculus of Variations Critical Points for Pairs of Functionals and Semilinear Elliptic Equations Front Propagation in Diffusion Problems on Trees A Gamma Limit Approach for Viscosity Stationary Solutions of a Model Convection Equation

Nonlinear Partial Differential Equations and Their Application - D.Cioranescu (EX)

Author

D Cioranescu
J.L. Lions

Cover Price : Rs 4,995.00

Imprint : CRC / Lewis
ISBN : 9780582369269
YOP : 2014

Binding : Hardback
Total Pages : 352
CD : No

ABOUT THIS VOLUME This book contains the texts of selected lectures delivered by leading international experts at the well-established weekly seminar held at the College de France. The main theme of the Seminar is recent work in the field of nonlinear partial differential equations – a field of growing importance, both in pure and applied mathematics. The emphasis is laid on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis and engineering. Volume XIII of the College de France Seminar proceedings will be of particular interest to postgraduate students and specialists in these areas. PITMAN RESEARCH NOTES IN MATHEMATICS SERIES The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline. The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by Mathematical Review. This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph. Will also be considered for a place in the series. Normally homograph, material is required, even if written by more than one author, thus multi-author works will be included provided that there is a strong linking theme or editorial pattern. Contents Preface A Nonlinear Lax-Milgram Lemma Arising in the Modeling of Elastomers. Regularity for Solutions to the Equation of Surfaces of Prescribed Mean Curvature Using the Coarea Formula. H-Convergence for Perforated Domains. Some Mathematical Problems in Marine Modelling. A Modelling of the Stability of Aluminium Electrolysis Cells. Dense Oscillations for the Compressible 2-d Euler Equations. The Hysteretic Event in the Computation of Magnetism and Magnetostriction. From Three-Dimensional Elasticity to the Nonlinear Membrane Model. Turbulence et structures cohérentes dans les fluides. Construction d'une base spéciale pour la résolution de quelques problèmes non linéaires d'Oceanographie physique en dimension deux. Homogenization of Lattice-Like Domains: L-Convergence. Time Decays: An Analogy between Kinetic Transport, Schrödinger and Gas Dynamics Equations. Théorème d'unicité et contrôle pour les équations hyperboliques. Shock Waves in General Relativity - A Generalization of the Oppenheimer-Snyder Model for Gravitational Collapse. Nonlinear Wave Equations. Mathematical Models of Hysteresis - A Survey.

Ordinary and Partial Differential Equations, Indian Reprint 2014 - B.D.Sleeman (EX)

Author

B.D. Sleeman
R.J. Jarvis

Cover Price : Rs 4,995.00

Imprint : CRC / Lewis
ISBN : 9780582091375
YOP : 2014

Binding : Hardback
Total Pages : 304
CD : No

ABOUT THIS VOLUME This volume arises from the twelfth Dundee Conference on Ordinary and Partial differential Equations held at the University of Dundee in June 1992. It contains papers by a number of experts. Special emphasis is given to recent developments in the asymptotic behaviour of solutions to differential equations, scattering theory and neural system. Of particular note is a comprehensive survey of major contributions to the study of counting function asymptotics for fractal domains. Topics covered include direct and inverse scattering problems, asymptotic expansions and Stokes phenomenon, the Wey I-Berry conjecture, pattern generation in neural systems, reactive transport and dispersal of waste, and integral inequalities. Readership: Graduate students and research workers in the theory of ordinary and partial differential equations, nonlinear analysis, applied mathematics and mathematical biology. PITMAN RESEARCH NOTES IN MATHEMATICS SERIES The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline. The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by Mathematical Review. This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph. Will also be considered for a place in the series. Normally homogeneous, material is required, even if written by more than one author, thus multi-author works will be included provided that there is a strong linking theme or editorial pattern. Contents Preface  The effect of nonlinearity on the scattering of sound by lightly loaded thin elastic structures, I D Abrahams  Analytic and numerical aspects of the HELP integral inequality, W N Everitt  Some reactive transport, dispersal and flow problems associated with geological disposal of radioactive waste, P Grindrod  Central pattern generators in neural systems, oscillations, bifurcations and coupled nonlinear oscillators, A V Holden and Julie Hyde  Numerical algorithms in inverse scattering theory, A Kirsch  Asymptotic series and remainders, D S Jones  Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media and the Weyl-Berry conjecture, M L Lapidus  Fourier Asymptotics, J Lighthill  Inverse Fourier asymptotics, J Lighthill  Exponentially-improved asymptotic solutions of ordinary differential equations, F W J Olver  Scattering from unbounded surfaces, G F Roach

Introduction to Mathematical Population Dynamics - Mimmo Iannelli

Author

Mimmo Iannelli
Andrea Pugliese

Cover Price : Euro 59.99

Imprint : Springer
ISBN : 9783319030258
YOP : 2014

Binding : Paperback
Total Pages : 356
CD : No

This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides up-to-date developments in several areas. CONTENTS Part I The growth of a single population 1 Malthus, Verhulst and all that 2 Population models with delays 3 Models of discrete-time population growth 4 Stochastic modeling of population growth 5 Spatial spread of a population Part II Multispecies Models 6 Predator-prey models 7 Competition among species 8 Mathematical modeling of epidemics 9 Models with several species and trophic levels Appendix A. Basic theory of Ordinary Differential Equations Appendix B. Delay Equations Appendix C. Discrete dynamics Appendix D. Continuous-time Markov chains References

Primer of Algebraic Geometry, Indian Reprint - Huishi Li (EX)

Author

Huishi Li
Freddy Van Oystaeyen

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824703747
YOP : 2015

Binding : Hardback
Total Pages : 384
CD : No

About the Book Written for senior undergraduate and first-year graduate students, as well as a refresher for seasoned mathematicians, A Primer of Algebraic Geometry presents a systematic treatment of elementary algebraic geometry, offering algebraic structure theory in an "effective" way - covering dimension theory for varieties that agree with the use of the Zariski topology. Emphasizing the new Groebner basis method that relies on the ordered ideal structure theory in polynomial rings and the Weierstrass theory of elliptic curves, topics in A Primer of Algebraic Geometry range from polynomials and affine space to radical ideals and the Nullstellensatz, from the Zariski topology and irreducible algebraic sets to rational functions and local rings. From projective space to multiprojective space and Segre product, from monomial orderings to Hilbert basis theorem and Groebner basis, from the algebraic set of a monomial ideal to the topological dimension of an affine algebraic set, from regular functions on varieties to nonsingular points in algebraic sets from nonsingular curves to the Riemann-Roch theorem, from the standard form of a cubic nonsingular curve to elliptic functions and Weierstrass theory, and more. "A self-contained resource complete with exercises in each section, a Primer of Algebraic Geometry is a reference for pure and applied mathematicians, algebraists, number theorists, algebraic geometers, and computer scientists, and an out standing text for upper-level undergraduate and graduate students with an interest in computer algebra, robotics and computational geometry, theoretical computer science, and mathematical methods of technology. Contents Ch. I. Affine Algebraic Sets and the Nullstellensatz Ch. II. Polynomial and Rational Functions Ch. III. Projective Algebraic Sets Ch. IV. Groebner Basis Ch. V. Dimension of Algebraic Sets Ch. VI. Introduction to Local Theory Ch. VII. Curves Ch. VIII. Elliptic Curves App. I. Finiteness Conditions and Field Extensions App. II. Localization, Discrete Valuation Rings and Dedekind Domains. References Index About the Authors Huishi Li is Assistant Professor of Mathematics at Bilkent University, Turkey. Previously he was Professor of Mathematics at the Shaanxi Normal University, People’s Republic of China. The author or coauthor of several articles, he is coauthor with Professor Van Oystaeyen of Zariskian Filtrations. Dr. Li received the Ph.D degree (1990) in mathematics from the University of Antwerp /UIA, Belgium. Freddy Van Oystaeyen is a Professor of Mathematics at the University of Antwerp/UIA in Belgium. The author, coauthor, editor, or coeditor of over 200 articles, proceedings. Book chapters, and books, including Brauer Groups and the Cohomology of Graded Rings and Commutative Algebra and Algebraic Geometry (both titles, Marcel Dekker, Inc.), he is a board member of the Belgium Mathematical Society. Professor Van Oystaeyen received the Ph.D.degree (1972) in mathematics from the free University of Amsterdam, The Netherlands, and the Habilitation degree (1975) from the University of Antwerp/UIA, Belgium.

Topological Vector Spaces,2nd ed, Indian Reprint - Lawrence Narici (EX)

Author

Lawrence Narici
Edward Beckenstein

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584888666
YOP : 2015

Binding : Hardback
Total Pages : 628
CD : No

With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn–Banach theorem. This edition explores the theorem’s connection with the axiom of choice, discusses the uniqueness of Hahn–Banach extensions, and includes an entirely new chapter on vector-valued Hahn–Banach theorems. It also considers different approaches to the Banach–Stone theorem as well as variations of the theorem. The book covers locally convex spaces; barreled, bornological, and webbed spaces; and reflexivity. It traces the development of various theorems from their earliest beginnings to present day, providing historical notes to place the results in context. The authors also chronicle the lives of key mathematicians, including Stefan Banach and Eduard Helly. Features - Provides extensive coverage of the Hahn-Banach and Banach-Stone theorems - Discusses the evolution of the Hahn-Banach theorem and Eduard Helly’s considerable contribution to it. - Presents historical notes on the development of many important theorems and the people who discovered and proved them, including The Scottish Café group - Includes numerous end-of-chapter exercises, a broad spectrum of examples, and detailed proofs Suitable for both beginners and experienced researchers, this book contains an abundance of examples, exercises of varying levels of difficulty with many hints, and an extensive bibliography and index. Contents Background Commutative Topological Groups Completeness Topological Vector Spaces Locally Convex Spaces and Seminorms Bounded Sets Hahn–Banach Theorems Duality Krein–Milman and Banach–Stone Theorems Vector-Valued Hahn–Banach Theorems Barreled Spaces Inductive Limits Bornological Spaces Closed Graph Theorems Reflexivity Norm Convexities and Approximation Bibliography Index

Number Theory, Indian Reprint, Don Redmond (EX)

Author

Don Redmond

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824796969
YOP : 2015

Binding : Hardback
Total Pages : 764
CD : No

About the Book… This reference/text provides a detailed introduction to number theory and demonstrates how other areas of mathematics enter into the study of the properties of natural numbers. Offering helpful problem sets within each section and at the end of each chapter to reinforce essential concepts, Number Theory contains up-to-date information on divisibility properties…. polynomial congruence, the sums of squares and trigonometric sum… Diophantine approximation …the behavior of prime numbers….algebraic number fields…and more. Furnishing a useful bibliography, allowing reader to further investigate the results presented, Number Theory is an ideal reference for research mathematicians in terested in algebra and number theory, and a valuable text for upper-level under-graduate and graduate students in these disciplines. Contents Preface A Historical Introduction Primes and Divisibility Congruences Quadratic Residues Approximation of Real Numbers Diophantine Equations I Diophantine Equations II Arithmetic Functions The Average Order of Arithmetic Functions Prime Number Theory An Introduction to Algebraic Number Theory. Tables Bibliography Index About the Author Don Redmond is an Associate Professor in the Mathematics Department at Southern Illinois university at Carbondale. Dr. Redmond is a member of the American Mathematical Society, the Mathematical Association of America, the National Council of Teachers of Mathematics, and Sigma Xi. He received the Ph.D degree (1976) in mathematics from the University of Illinois at Urbana Champaign.

Introduction to Fourier Series, Indian Reprint - Rupert Lasser (EX)

Author

Rupert Lasser

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824796105
YOP : 2015

Binding : Hardback
Total Pages : 294
CD : No

This concise, self-contained reference/text addresses all of the major topics in Fourier series - emphasizing the concept of approximate identities; presenting applications, particularly in time series analysis; stressing throughout the idea of homogeneous Banach spaces; and providing new results. Utilizing techniques from functional analysis and measure theory, Introduction to Fourier Series furnishes representation theorems such as Herglotz's theorem and Wiener's theorem...compares the performance of approximate identities with elements of best approximation...develops results on spectral synthesis applying Banach algebra techniques...derives characterizations of absolute convergence of Fourier series...studies Fourier and Plancherel transformations on the real axis establishing the relation to Fourier series using the Poisson summation formula...and more. Written by an internationally recognized expert, Introduction to Fourier Series is an incomparable reference for pure and applied mathematicians and signal processing engineers and the text of choice for all upper-level undergraduate and graduate students taking courses in Fourier analysis, harmonic analysis, or approximation theory with a basic knowledge of real and abstract analysis. Contents Fourier Coefficients Approximate Identities Approximate Identities and Pointwise Convergence Square Integrable Functions Convergence of Fourier Series in Norm Local Convergence Characterization of Fourier Coefficients Hilbert Transform Characterizations Of Approximate Identities. Triangular Schemes Elements of Best Approximation Poisson Integrals and Hardy Spaces Conjugation of Approximate Identities Szego-Kolmogoriv-Theorem Absolute convergence of Fourier series Fourier Transform on R Plancherel Transform on R Poisson Summation Formula Appendices Appendix A: Measure Theory Appendix B: Banach Spaces Appendix C: Banach Algebras Referemces Index

Differential Forms on Singular Varieties, Indian Reprint - Vincenzo Ancona (EX)

Author

Vincenzo Ancona
Bernard Gaveau

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780849337390
YOP : 2015

Binding : Hardback
Total Pages : 332
CD : No

The cohomology of a singular complex space cannot carry a pure hodge structure -it must be a mixed Hodge structure, wherein the weight filtration of Deligne and Grothendieck induces a graduation on the cohomology, and each quotient space of the graduation carrier a pure Hodge structure. While it is relatively easy to explain the mixed Hodge structure on the cohomology of an algebraic manifold it is not so straightforward for a singular space. The weight filtration constructured by Deligne using the “descente cohomologique” make it difficult to see how the mixed Hodge structure is made. Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher dimension than the initial space. It simplifies the theory through easily identifiable and well-defined weight filtration, and to maintain accessibility,It also avoids discussion of cohomological descent theory. The treatment is self-contained and brings together information that allows readers to follow and understand this difficult but important subject without jumping from one reference to another. Features - Provides a clear, self-contained treatment of classical Hodge theory on manifolds, including complex manifolds, Khaeler manifolds, and De Rham theory - Offers a particularly elegant explanation to the singular analogue of De Rham theory on manifolds - Summarizes topics such as sheaf theory, cohomology, and complex spaces, important in many branches of mathematics - Features an approach to mixed Hodge structures that employs recursive arguments on dimension Contents Classical Hodge Theory. Spectral Sequences and Mixed Hodge Structures. Complex Manifolds, Vector Bundles, Differential Forms. Sheaves and Cohomology. Harmonic Forms on Hermitian Manifolds. Hodge Theory on Compact Kählerian Manifolds. The Theory of Residues on a Smooth Divisor. Complex Spaces. Differential Forms on Complex Spaces. The Basic Example. Differential Forms in Complex Spaces. Mixed Hodge Structures on Compact Spaces. Mixed Hodge Structures on Noncompact Spaces. Residues and Hodge Mixed Structures: Leray Theory. Residues and Mixed Hodge Structures on Noncompact Manifolds. Mixed Hodge Structures in Noncompact Spaces: The Basic Example. Mixed Hodge Structures on Noncompact Singular Spaces. References Vincenzo Ancona is a professor in the Department of Mathematics, University of Firenze, Italy. Bernard Gaveau is a professor in the Department of Mathematics, University Pierre et Marie Curie, Paris, France.

Elements of Real Analysis, Indian Reprint - M.A.Al-Gwaiz (EX)

Author

M.A. Al-Gwaiz

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584886617
YOP : 2015

Binding : Hardback
Total Pages : 450
CD : No

Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a comprehensive introduction to analysis on the real line, The book prepares you for conducing analysis in higher dimensions and more abstract spaces by building up the analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, addressing theorems like mean value, inverse function, Taylor’s, and weierstrass approximation. The final chapters focus on the more advanced theory of Lebesgue measure and integration. Requiring only basic knowledge of elementary calculus, this book presents the necessary material for students and professionals in various mathematics related fields, such as engineering, statistics, computer science, to explore real analysis. Features - Presents a foundation in real analysis, starting with the basics and gently progressing to more computer topics - Covers the real number system, sequences, and infinite series - Explores functions, limits, continuity, differentiability, and integration, including Riemann integrals - Includes sequences and series of functions and their modes of convergence, naturally building on the properties of numerical sequences and series - Provides an introduction to advanced probability and stochastic theory by including two chapters on Lebesgue and integration Contents Preface preliminaries Real Numbers Sequences Infinite Series Limit of a Function Continuity Differentiation The Riemann Integral Sequences and Series of Functions Lebesgue Measure Lebesgue Integration References notation Index M.A.Al-Gwaiz and S.A.Elsanousi are mathematics professors at King Saud University, Riyadh, Saudi Arabia.

Algorithmic Lie Theory for Solving Ordinary Differential Equations , Indian Reprint - Fritz Schwarz (EX)

Author

Fritz Schwarz

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584888895
YOP : 2015

Binding : Hardback
Total Pages : 444
CD : No

Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results. After an introductory chapter, the book provides the mathematical foundation of linear differential equations, covering Loewy's theory and Janet bases. The following chapters present results from the theory of continuous groups of a 2-D manifold and discuss the close relation between Lie's symmetry analysis and the equivalence problem. The core chapters of the book identify the symmetry classes to which quasilinear equations of order two or three belong and transform these equations to canonical form. The final chapters solve the canonical equations and produce the general solutions whenever possible as well as provide concluding remarks. The appendices contain solutions to selected exercises, useful formulae, properties of ideals of monomials, Loewy decompositions, symmetries for equations from Kamke's collection, and a brief description of the software system ALLTYPES for solving concrete algebraic problems. Features - Explores two fundamental additions to Lie theory: Loewy’s theory of linear ODEs and Janet’s theory of linear PDEs - Discusses the close connection between Lie symmetries and closed form solutions - Includes numerous worked examples and problems, along with detailed solutions in an appendix - Provides a website that contains the software for performing lengthy algebraic calculations Contents INTRODUCTION LINEAR DIFFERENTIAL EQUATIONS Linear Ordinary Differential Equations Janet's Algorithm Properties of Janet Bases Solving Partial Differential Equations LIE TRANSFORMATION GROUPS Lie Groups and Transformation Groups Algebraic Properties of Vector Fields Group Actions in the Plane Classification of Lie Algebras and Lie Groups Lie Systems EQUIVALENCE AND INVARIANTS OF DIFFERENTIAL EQUATIONS Linear Equations Nonlinear First-Order Equations Nonlinear Equations of Second and Higher Order SYMMETRIES OF DIFFERENTIAL EQUATIONS Transformation of Differential Equations Symmetries of First-Order Equations Symmetries of Second-Order Equations Symmetries of Nonlinear Third-Order Equations Symmetries of Linearizable Equations TRANSFORMATION TO CANONICAL FORM First-Order Equations Second-Order Equations Nonlinear Third-Order Equations Linearizable Third-Order Equations SOLUTION ALGORITHMS First-Order Equations Second-Order Equations Nonlinear Equations of Third Order Linearizable Third-Order Equations CONCLUDING REMARKS A: Solutions to Selected Problems B: Collection of Useful Formulas C: Algebra of Monomials D: Loewy Decompositions of Kamke's Collection E: Symmetries of Kamke's Collection F: ALLTYPES Userinterface REFERENCES INDEX

Weakly Connected Nonlinear Systems, Indian Reprint - Anatoly Martynyuk (EX)

Author

Anatoly Martynyuk

Cover Price : Rs 3,995.00

Imprint : CRC Press
ISBN : 9781466570863
YOP : 2015

Binding : Hardback
Total Pages : 228
CD : No

Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations. After supplying the necessary mathematical foundation, the book illustrates recent approaches to studying the boundedness of motion of weakly connected nonlinear systems. The authors consider conditions for asymptotic and uniform stability using the auxiliary vector Lyapunov functions and explore the polystability of the motion of a nonlinear system with a small parameter. Using the generalization of the direct Lyapunov method with the asymptotic method of nonlinear mechanics, they then study the stability of solutions for nonlinear systems with small perturbing forces. They also present fundamental results on the boundedness and stability of systems in Banach spaces with weakly connected subsystems through the generalization of the direct Lyapunov method, using both vector and matrix-valued auxiliary functions. Designed for researchers and graduate students working on systems with a small parameter, this book will help readers get up to date on the knowledge required to start research in this area. Contents Preface Acknowledgments Preliminaries Introductory Remarks Fundamental Inequalities Stability in the Sense of Lyapunov Comparison Principle Stability of Systems with a Small Parameter Comments and References Analysis of the Boundedness of Motion Introductory Remarks Statement of the Problem μ-Boundedness with Respect to Two Measures Boundedness and the Comparison Technique Boundedness with Respect to a Part of Variables Algebraic Conditions of μ-Boundedness Applications Comments and References Analysis of the Stability of Motion Introductory Remarks Statement of the Problem Stability with Respect to Two Measures Equistability via Scalar Comparison Equations Dynamic Behavior of an Individual Subsystem Asymptotic Behavior Polystability of Motion Applications Comments and References Stability of Weakly Perturbed Systems Introductory Remarks Averaging and Stability Stability on a Finite Time Interval Methods of Application of Auxiliary Systems Systems with Nonasymptotically Stable Subsystems Stability with Respect to a Part of Variables Applications Comments and References Stability of Systems in Banach Spaces Introductory Remarks Preliminary Results Statement of the Problem Generalized Direct Lyapunov Method μ-Stability of Motion of Weakly Connected Systems Stability Analysis of a Two-Component System Comments and References Bibliography Index

Measure Theory and Integration, Indian Reprint - M.M.Rao (EX)

Author

M.M. Rao

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824754013
YOP : 2015

Binding : Hardback
Total Pages : 782
CD : No

About the Book… Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using offering valuable examples, exercises, and applications. Examines the Henstock-Kurzweil integral with approaches not found in any other text. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, including a new chapter on nonabsolute integrals…contains extended discussions on the four basic results of Banach spaces… presents an in-depth analysis of the classical integrals with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties… details the basic properties and extensions of the Lebesgue-Caratheaodory measure theory, as well as the structure and convergence of real measurable functions…and covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Contents Preface to the Second Edition Preface to the First Edition Introduction and Preliminaries Measurability and Measures Measurable Functions Classical Integration Differentiation and Duality Product Measures and Integrals Nonabsolute Integration Capacity Theory and Integration The Lifting Theorem Topological Measures Some Complements and Applications Appendix References Index of Symbols and Notation Author Index Subject Index About the Autor… M.M.Rao is Professor of Mathematics, University of California, Riverside, The author, coauthor, editor, or coeditor of numerous professional papers, monographs, and books, including Applications of Orlicz Spaces, Theory of Orlicz Spaces, and Conditional Measures and Applications (all titles, Marcel Dekker, Inc.), he is a Fellow of the Institute of Mathematical Statistics and the American Association for the Advancement of Science and a member of the American Mathematical Society and the International Statistical Institute. He received the B.A.degree (1949) from Andhra University, India, the M.A.(1952) and M.Sc. (1955) degrees from the University of Madras, India, and the Ph.D.degree (1959) from the University of Minnesots, Minneaplis.

C*-Algebras and Numerical Analysis, Indian Reprin - Ronald Hagen (EX)

Author

Roland Hagen
Steffen Roch
Bernd Silbermann

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824704605
YOP : 2015

Binding : Hardback
Total Pages : 384
CD : No

This book examines the relationship between C*-algebras and numerical analysis; discusses fractality-covering asymptotic properties of approximation operators, such as stability, regularizability behavior of condition numbers, eigenvalues, pseudoeigen values, singular values, and Rayleigh quotients; and describes fredholmness- focusing on algebras that arise from concrete approximation methods. Featuring more than 1000 mathematical expressions, C*- Algebras and Numerical Analysis presents Arveson’s results culminating in a generalization of the Szego limit theorem… introduces kernel and cokernel dimension for approximation sequences… outlines the lifting theorem and the structure of fractal lifting homomorphisms studies piecewise continuous and quasicontinuous coefficients … details polynomial collocation and finite sections of band dominated … considers spectra, pseudospectra, numerical ranges and their limiting sets… spotlights Moore-Penrose inverses and regularization of matrices and operators… surveys finite sections to Toeplitz operators… and more. Contents Preface Introduction - The algebraic language of numerical analysis - Regularization of approximation methods - Approximation of spectra - Stability analysis for concrete approximation methods - Representation theory - Fredholm sequences - Self-adjoint approximation sequences Bibliography Index About the Author Ronald Hagen Is Teacher of Mathematics at Freies Gymnasium Penig, Penig, Germany, The author or coauthor of over 20 professional publications. Dr. Hagen received the Diploma in mathematics and the Teacher’s Diploma (1976 ) from the State University, Odessa, Russia, and the Ph.D. degree from the Teachnische Hochschule, Karl-Marx-Stadt, Germay. Steffen Roch is a Lectures at the Technical University of Darmastadt, Germany, The author or coauthor of over 50 peer-reviewed articles, Dr. Roch received the Diploma in mathematics (1982) and the Ph.D. degree (1988) from the Technische Hochschule, Karl-Marx-Stadt, Germany, and the Habilitation (1992) from the Technical University, Chemnitz, Germany. Bernd Silbermann is Professor of Mathematics, Technical University, Cheminitz, Germany. The coauthor of six monographs in operator theory and numerical analysis, Dr. Silbermann received the Diploma in mathematics (1967) from Lomonossov University, Moscow, Russia, and the Ph.D. degree (1970) and Habilitation (1974) from the Technische Hochschule,Karl-Marx-Stadt, Germany.

Matrix Theory, Indian Reprint - Robert Piziak (EX)

Author

Robert Piziak
P.L. Odell

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584886259
YOP : 2015

Binding : Hardback
Total Pages : 568
CD : No

Highlighting the generalized inverse of a matrix and the method of full rank factorization, Matrix Theory: From Generalized Inverses to Jordan Form probes introductory as well as more sophisticated linear algebra concepts. This presentation helps connect linear algebra to more advanced abstract algebra and matrix theory. The book first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses, including the Moore-Penrose inverse. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. Always mathematically constructive, this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra. Features -Focuses on the development of the Moore-Penrose inverse, offering excellent preparation for work on advanced treatises -Uses concrete examples to make arguments more clear -Presents MATLAB examples and exercises throughout since it is often used when dealing with matrices -Includes appendices that review basics linear algebra and related prerequisites -Provides numerous homework Problem and suggestions for further reading Contents THE IDEA OF INVERSE Solving Systems of Linear Equations The Special Case of "Square" Systems GENERATING INVERTIBLE MATRICES A Brief Review of Gauss Elimination with Back Substitution Elementary Matrices The LU and LDU Factorization The Adjugate of a Matrix The Frame Algorithm and the Cayley-Hamilton Theorem SUBSPACES ASSOCIATED TO MATRICES Fundamental Subspaces A Deeper Look at Rank Direct Sums and Idempotents The Index of a Square Matrix Left and Right Inverses THE MOORE-PENROSE INVERSE Row Reduced Echelon Form and Matrix Equivalence The Hermite Echelon Form Full Rank Factorization The Moore-Penrose Inverse Solving Systems of Linear Equations Schur Complements Again GENERALIZED INVERSES The {1}-Inverse {1,2}-Inverses Constructing Other Generalized Inverses {2}-Inverses The Drazin Inverse The Group Inverse NORMS The Normed Linear Space Cn Matrix Norms INNER PRODUCTS The Inner Product Space Cn Orthogonal Sets of Vectors in Cn QR Factorization A Fundamental Theorem of Linear Algebra Minimum Norm Solutions Least Squares PROJECTIONS Orthogonal Projections The Geometry of Subspaces and the Algebra of Projections The Fundamental Projections of a Matrix Full Rank Factorizations of Projections Affine Projections Quotient Spaces SPECTRAL THEORY Eigenstuff The Spectral Theorem The Square Root and Polar Decomposition Theorems MATRIX DIAGONALIZATION Diagonalization with Respect to Equivalence Diagonalization with Respect to Similarity Diagonalization with Respect to a Unitary The Singular Value Decomposition JORDAN CANONICAL FORM Jordan Form and Generalized Eigenvectors The Smith Normal Form MULTILINEAR MATTERS Bilinear Forms Matrices Associated to Bilinear Forms Orthogonality Symmetric Bilinear Forms Congruence and Symmetric Matrices Skew-Symmetric Bilinear Forms Tensor Products of Matrices APPENDIX A: COMPLEX NUMBERS What is a Scalar? The System of Complex Numbers The Rules of Arithmetic in C Complex Conjugation, Modulus, and Distance The Polar Form of Complex Numbers Polynomials over C Postscript APPENDIX B: BASIC MATRIX OPERATIONS Introduction Matrix Addition Scalar Multiplication Matrix Multiplication Transpose Submatrices APPENDIX C: DETERMINANTS Motivation Defining Determinants Some Theorems about Determinants The Trace of a Square Matrix APPENDIX D: A REVIEW OF BASICS Spanning Linear Independence Basis and Dimension Change of Basis INDEX

Linear Algebra Over Commutative Rings, Indian Reprint - Bernard R.McDonald (EX)

Author

Bernard R. McDonald

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824771225
YOP : 2015

Binding : Hardback
Total Pages : 554
CD : No

About the Book Linear Algebra Over Commutative Rings provides an ideal, comprehensive introduction to and an up-to-date survey of matrix theory, linear algebra, and projective modules and their endomorphisms over commutative rings. Utilizing a commutative scalar ring for the matrices discusses, this volume fully describes: matrix theory over commutative rings… the theory of solutions of systems of linear equations… the structure of the general linear group…free modules and projective modules… the Morita duality and the Baer correspondences of endomorphism rings… the automorphism theory of endomorphism ring… localization and the structure of projective modules including a proof of Serre’s Theorem… the theory of single endomorphism with an analysis of similarity, trace, determinant, characteristic polynomial, equivalence, and determinant-trace polynomials… and basic results in the K-theory of projective modules and the K-theory of their endomorphism rings. Contents PREFACE 1. MATRIX THEORY OVER COMMUTATIVE RINGS 2. FREE MODULES 3. THE ENDOMORPHIS RING OF A PROJECTIVE MODULE 4. PROJECTIVE MODULES 5. THEORY OF A SINGLE ENDOMORPHISM BIBLIOGRAPHY INDEX About the Author BERNARD R.MCDONALD is Program Director for Algebra and Number theory for the Division of Mathematical Sciences of the National Science Foundation, Washington, D.C.Prior to this position, Dr.McDonald was professor and chairman of the Dept of Mathematics at the University of Oklahoma, Norman . Dr. McDonald’s research interests include the study of commutative algebra, linear and geometric algebra, quadratic form and combinatorics. He is the author of Geometric Algebra Over Local Rings and Finite Rings with Identity, editor of Ring Theory and Algebra III: Proceedings of the Third Oklahoma Conference, coeditor (with Robert A.Morris) of Ring Theory II: Proceedings of the Social Oklahoma Conference and (With Andy R. Magid and Kirby C. Smith) of Ring Theory: Proceedings of the Oklahoma Conference (all titles, Marcel Dekker,Inc.) and has published articles in various mathematical journals. Dr.McDonald is a member of the American Mathematical Society and the Mathematical Association of America. He received the Ph.D.degree (1968) from Michigan State University.

General Topology - John L.Kelley

Author

John L. Kelley

Cover Price : Rs 695.00

Imprint : Springer
ISBN : 9781493975167
YOP : 2017

Binding : Paperback
Total Pages : 312
CD : No

John L.Kelley received his Ph.D.from The University of Virginia in 1940. He taught at Notre Dame University and the University of Chicago prior to coming to the University of California at Berkeley. Since coming to Berkeley he has held visiting appointments at Tulane University, the University of Kansas, Cambridge University (as Fullbright Research Professor), and the Indian Institute of Technology at Kanpur. Professor Kelley is the author of several books and research articles on topology and functional analysis. CONTENTS Preliminaries 1. Topological Spaces 2. Moore-Smith Convergence 3. Product and Quotient Spaces 4. Embedding and Metrization 5. Compact Spaces 6. Uniform Spaces 7. Function Spaces Appendix: Elementary Set Theory

Graph Theory - J.A.Bondy

Author

J.A. Bondy
U.S.R Murty

Cover Price : Rs 995.00

Imprint : Springer
ISBN : 9781447173601
YOP : 2017

Binding : Paperback
Total Pages : 668
CD : No

Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics - computer science, combinatorial optimization, and operations research in particular -but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance. The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises - of varying levels of difficulty - are provided to help the reader master the techniques and reinforce their grasp of the material. A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters. Contents 1 Graphs 2 Subgraphs 3 Connected Graphs 4 Trees 5 Nonseparable Graphs 6 Tree-Search Algorithms 7 Flows in Networks 8 Complexity of Algorithms 9 Connectivity 10 Planar Graphs 11 The Four-Colour Problem 12 Stable Sets and Cliques 13 The Probabilistic Method 14 Vertex Colourings 15 Colourings of Maps 16 Matchings 17 Edge Colourings XII Contents 18 Hamilton Cycles 19 Coverings and Packings in Directed Graphs 20 Electrical Networks 21 Integer Flows and Coverings Unsolved Problems References General Mathematical Notation Graph Parameters Operations and Relations Families of Graphs Structures Other Notation Index

Frontiers in Interpolation and Approximation - N.K.Govil

Author

N.K. Govil
H.N. Mhaskar
Ram N. Mohapatra
Zuhair Nashed

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584886365
YOP : 2015

Binding : Hardback
Total Pages : 497
CD : No

Dedicated to the memory of the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation is a collection of papers by mathematicians with international reputations in several areas of approximation theory, interpolation theory, and classical analysis. Some of the topics covered are the theory of multivariate polynomial, approximation inequalities for multivariate polynomials, exponential sums, the linear combination of Gaussians, orthogonal polynomials and their zeroes, uncertainty principles in wavelet analysis, approximation on the sphere, interpolation in the complex domain, weighted approximation on an infinite interval, and abstract approximation theory. Features - Present complex interpolation by algebraic and trigonometric polynomials and transcendental entire functions - Investigates the optimality of uncertainty products - Proposes alternatives to interpolation including hyperinterpolation and quasi-interpolation on the sphere and Euclidean spaces - Provides fast algorithms for approximation on the sphere Containing both original research and comprehensive surveys, this book will be valuable to researchers and graduate students by offering many important results of interpolation and approximation. Contents Foreword Preface Editors Contributors Ambikeshwar Sharma Markov-Type Inequalities for Homogeneous Polynomials on Nonsymmetric Star-Like Domains Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions The Norm of an Interpolation Operator on H8(D) Sharma and Interpolation, 1993-2003: The Dutch Connection Freeness of Spline Modules from a Divided to a Subdivided Domain Measures of Smoothness on the Sphere Quadrature Formulae of Maximal Trigonometric Degree of Precision Inequalities for Exponential Sums via Interpolation and Turán-Type Reverse Markov Inequalities Asymptotic Optimality in Time-Frequency Localization of Scaling Functions and Wavelets Interpolation by Polynomials and Transcendental Entire Functions Hyperinterpolation on the Sphere Lagrange Interpolation at Lacunary Roots of Unity A Fast Algorithm for Spherical Basis Approximation Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights having Zeros Fourier Sums and Lagrange Interpolation on (0,+8) and (-8,+8) On Bounded Interpolatory and Quasi-Interpolatory Polynomial Operators Hausdorff Strong Uniqueness in Simultaneous Approximation Zeros of Polynomials Given as an Orthogonal Expansion Uniqueness of Tchebycheff Spaces and their Ideal Relatives Index

Moving Shape Analysis and Control

Author

Marwan Moubachir
Jean-Paul Zolesio

Cover Price : Rs 4,995.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9781584886112
YOP : 2015

Binding : Hardback
Total Pages : 312
CD : No

Problems involving the evolution of two- and three-dimensional domains arise in many areas of science and engineering. These range from free surface flows, phase changes, and fracture and contact problems to applications in civil engineering construction, biomechanical systems, and computer vision. Emphasizing an Eulerian approach, Moving Shape Analysis and Control: Applications to Fluid Structure Interactions presents valuable tools for the mathematical analysis of evolving domains. The book illustrates the efficiency of the tools presented through different examples connected to the analysis of noncylindrical partial differential equations , such as Navier–Stokes equations for incompressible fluids in moving domains. The authors begin by providing all of the details of existence and uniqueness of the flow in both strong and weak cases. After establishing several important principles and methods, they devote several chapters to demonstrating Eulerian evolution and derivation tools for the control of systems involving fluids and solids. The book concludes with boundary control of fluid–structure interaction systems, followed by helpful appendices that review some of the advanced mathematics used throughout the text. Offering new, robust approaches to evolving domains, this book… - Provides various tool to handle moving domains on the level of intrinsic definition, computation, optimization, and control - Addresses real-world engineering problems with applications - Emphasizes the Eulerian approach using evolution and derivation tools for controlling fluids and systems - Includes two chapters devoted to fluid control described using Navier-Stokes equations - Features new approaches to deal with boundary control fluid-structure interaction systems Contents Introduction Classical and Moving Shape Analysis Fluid–Structure Interaction Problems Plan of the Book Detailed Overview of the Book An Introductory Example: The Inverse Stefan Problem The Mechanical and Mathematical Settings The Inverse Problem Setting The Eulerian Derivative and the Transverse Field The Eulerian Material Derivative of the State The Eulerian Partial Derivative of the State The Adjoint State and the Adjoint Transverse Field Weak Evolution of Sets and Tube Derivatives Introduction Weak Convection of Characteristic Functions Tube Evolution in the Context of Optimization Problems Tube Derivative Concepts A First Example: Optimal Trajectory Problem Shape Differential Equation and Level Set Formulation Introduction Classical Shape Differential Equation Setting The Shape Control Problem The Asymptotic Behavior Shape Differential Equation for the Laplace Equation Shape Differential Equation in Rd+1 The Level Set Formulation Dynamical Shape Control of the Navier–Stokes Equations Introduction Problem Statement Elements of Noncylindrical Shape Calculus Elements of Tangential Calculus State Derivative Strategy Min-Max and Function Space Parameterization Min-Max and Function Space Embedding Conclusion Tube Derivative in a Lagrangian Setting Introduction Evolution Maps Navier–Stokes Equations in Moving Domain Sensitivity Analysis for a Simple Fluid–Solid Interaction System Introduction Mathematical Settings Well-Posedness of the Coupled System Inverse Problem Settings KKT Optimality Conditions Conclusion Sensitivity Analysis for a General Fluid–Structure Interaction System Introduction Mechanical Problem and Main Result KKT Optimality Conditions Appendix A: Functional Spaces and Regularity of Domains Appendix B: Distribution Spaces Appendix C: The Fourier Transform Appendix D: Sobolev Spaces References Index

Linear Systems and Control - Martin J.Corless

Author

Martin J. Corless
Arthur E. Frazho

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824707293
YOP : 2015

Binding : Hardback
Total Pages : 352
CD : No

Based largely on state space models, this text/reference utilizes fundamental linear algebra and operator techniques to develop classical and modern results in linear systems analysis and control design. Linear Systems and Control presents stability and performance results for linear systems… provides a geometric perspective on controllability and observability….develops state space realizations of transfer functions…. studies stabilizability and detectability…. constructs state feedback controllers and asymptotic state estimators…. covers the linear quadratic regulator problem in detail….offers an introduction to H-infinity control…. and presents results on Hamiltonian matrices and Riccati equations. CONTENTS Preface Systems and Contol Stability Lyapunov Theory Observability Controllability Controllable and Observable Realizations More Realization Theory State Feedback and Stabilizability State Estimators and Detectability Output Feedback Controllers Zeros of Transfer Functions Linear Quadratic Regulators The Hamilitonian Matrix and Riccati Equations H∞ Analysis H∞ Control Appendix: Least Squares Bibliography Index About the Authors…. Martin J.Corless is a Professor in the Department of Aeronautics and Astronautics, purdue University, West Lafayette, Indiana. He Received the B.E.degree (1977) in mechanical engineering from university the B.E.degree (1977) in mechanical engineering from University College, Dublin, Ireland, and the Ph.D. degree (1984) in mechanical engineering from the University of California, Berkeley. Arthure E. Frazho is a Professor in the Department of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana. He received the B.S.E. degree(1973) and the M.S.E. (1974) and the Ph.D.(1977) degrees in computer information and control engineering from the University of Michigan, Ann Arbor.

Discrete Geometry - Andras Bezdek

Author

Andras Bezdek

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824709686
YOP : 2015

Binding : Hardback
Total Pages : 480
CD : No

Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity- featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies…., arrangements on the sphere…. line transversals…. Euclidean and spherical tilings… geometric graphs…. polygons and polyhedral… and fixing systems for convex figures. Offering research and contributions from more than 50 esteemed international authorities Discrete Geometry is a fascinating collection for pure and applied mathematicians, geometers, topologists, combinatorialists, and upper-level undergraduate and graduate students in these disciplines. Contents Preface Contributors Biographical notes and work of W.Kuperberg Andras Bezdek and Gabor Fejes Toth - Transversal lines to lines and intervals, Jorge L. Arocha, Javier Bracho, and Luis Montejano - On a shortest path problem of G. Fejes, Toth Donald R. Baggett and Andras Bezdek - A short survey of (r,q)-structures, Vojtech Balint - Lattice points on the boundary of the integer hull, Imre Barany and Karoly Boroczky, Jr - The Erdos-Szekeres problem for planar points in arbitrary position, Tibor Bisztriczky and Gabor Fejes Toth - Separation in totally-sewn 4-polytopes, Tibor Bisztriczky and Deborah Oliveros - On a class of equifacetted polytopes, Gerd Blind and Roswitha Blind - Chessboard Ramsey numbers, Jens-P. Bode, Heiko Harborth, and Stefan Krause - Maximal primitive fixing systems for convex figures, Vladimir Boltyanski and Hernan Gonzalez-Aguilar - The Newton-Gregory problem revisited, Karoly Boroczky - Arrangements of 13 points on a sphere Karoly Boroczky and Laszlo Szabo - On point sets without k collinear points, Peter Brass - The Beckman-Quarles theorem for rational d-spaces, d even and d> 6, Robert Connelly and Joseph Zaks - Eedge-antipodal convex polytopes - a proof of Talata's conjecture, Balazs Csikos - Single-split tilings of the sphere with right triangles, Robert J. MacG. Dawson - Vertex-unfoldings of simplicial manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, and Joseph O'Rourke - View-obstruction through trajectories of co-dimension three Vishwa C. Dumir and Rajinder J. Hans-Gill - Fat 4-polytopes and fatter 3-spheres, David Eppstein, Greg Kuperberg, and Gunter M. Ziegler - Arbitrarily large neighbourly families of congruent symmetric convex 3-polytopes, Jeff Erickson and Scott Kim -On the non-solidity of some packings and coverings with circles, August Florian and Aladar Heppes -On the mth Petty numbers of normed spaces Karoly Bezdek, Marton Naszodi and Balazs Visy - Cubic polyhedra, Chaim Goodman-Strauss and John M. Sullivan -New uniform polyhedra, Branko Grunbaum - On the existence of a convex polygon with a specified number of interior points, Kiyoshi Hosono, Gyula Karolyi and Masatsugu Urabe - On-line 2-adic covering of the unit square by boxes, Janusz Januszewski and Marek Lassak - An example of a stable, even order quadrangle which is determined by its angle function, Janos Kincses -Sets with a unique extension to a set of constant width, Marton Naszodi and Balazs Visy - The number of simplices embracing the origin, Janos Pach and Mario Szegedy - Helly-type theorems on definite supporting lines for k-disjoint families of convex bodies in the plane, Sorin Revenko and Valeriu Soltan -Combinatorial aperiodicity of polyhedral prototiles, Egon Schulte - Sequences of smoothed polygons, G.C. Shephard - On a packing inequality, Graham, Witsenhausen and Zassenhaus, Jorg M. Wills - Covering a triangle with homothetic copies, Zoltan Furedi - Open problems, Andras Bezdek. Index About the Editor is Professor of Mathematics, Auburn University, Alabama, and Senior Research Fellow at the Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary. Previously, he held visiting position at Cornell University, Ithaca, New York, and the University of Calgary, Alberta, Canada. He received the Ph.D degree (1986) from Ohio State University, Columbus, and the Habilitation degree (1999) from Eotvos University, Budapest, Hungary.

Stochastic Versus Determininistic Systems of Differential Equations - G.S.Ladde

Author

G.S. Ladde
M. Sambandham

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824746971
YOP : 2015

Binding : Hardback
Total Pages : 336
CD : No

This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/fluctuations and parameter uncertainties both deterministic and stochastic. With numerical examples and figures embedded throughout the text, Stochastic Versus Deterministic Systems of Differential Equations scrutinizes random algebraic polynomials…explores the initial value problems (IVP) for ordinary differential systems with random parameters… investigates stochastic boundary value problems (SBVP) with random parameters… independently studies IVP and SBVP for ito-type stochastic differential systems…. Provides an integrated approach to stability, relative stability, and error estimate analysis…. explicitly illustrates the role of randomness and rate functions…. and interweaves presentation of methods with presentation of applications in population dynamics, hydrodynamics, and physics. Contents Preface Notation and Abbreviations Chapter 1: Random Polynomials Chapter 2: Ordinary Differential Systems with Random Parameters Chapter 3: Boundary Value Problems with Random Parameters Chapter 4: Ito-Type Stochastic Differential Systems Chapter 5: Boundary Value Problems of Ito-Type Appendix References Index About the Aurthor G.S.Ladde is Professor of Mathematics at The University of Texas at Arlington. The coauthor or coeditor of over nine books, including four monographs, Dr. Ladde has published more than 125 refereed research articles. He is the founder and coeditor of the journals Stochastic Analysis and Applications (Marcel Dekker, Inc.), and serves on several journal editorial boards. A Life Member of the American Mathematical Society, Sigma Xi, the Indian Mathematical Society, and the Marathwada Mathematical Society and a Senior Member of the Institute of Electrical and Electronics Engineers, Dr Ladde received the B.Sc degree (1963) from People’s College, Nanded , India the M.Sc.degree (1965) from Marathwada University, Aurangabad, India, and the Ph.D.degree (1972) from the University of Rhode Island, Kingston. M.Sambandham is Professor of Mathematics at Morehouse College, Atlanta, Georgia. In addition to coauthoring two monographs and publishing 75 refereed research articles, Dr. Sambandham serves as an editor for six international journals. His many professional membership include the American Mathematical Society and the Institute of Electrical and Electronics Engineers. Dr. Sambandham received the B.S.degree (1969) from the University of Madras, Chennai, India, and the M.Sc. (1971) and Ph.D. (1976) degrees from Annamalai University, Annamalai Nagar, India.

Advanced Mapping of Environmental Data - Mikhail Kanevski

Author

Mikhail Kanevski

Cover Price : Rs 4,995.00

Imprint : Wiley
ISBN : 9788126552023
YOP : 2015

Binding : Hardback
Total Pages : 328
CD : No

Contents Preface Chapter 1. Advanced Mapping of Environmental Data: Introduction M. KANEVSKI 1.1. Introduction 1.2. Environmental data analysis: problems and methodology 1.2.1. Spatial data analysis: typical problems 1.2.2. Spatial data analysis: methodology 1.2.3. Model assessment and model selection 1.3. Resources 1.3.1. Books, tutorials 1.3.2. Software 1.4. Conclusion 1.5. References Chapter 2. Environmental Monitoring Network Characterization and Clustering D. TUIA and M. KANEVSKI 2.1. Introduction 2.2. Spatial clustering and its consequences 2.2.1. Global parameters 2.2.2. Spatial predictions 2.3. Monitoring network quantification 2.3.1. Topological quantification 2.3.2. Global measures of clustering 2.3.2.1. Topological indices 2.3.2.2. Statistical indices 2.3.3. Dimensional resolution: fractal measures of clustering 2.3.3.1. Sandbox method 2.3.3.2. Box-counting method 2.3.3.3. Lacunarity 2.4. Validity domains 2.5. Indoor radon in Switzerland: an example of a real monitoring network 2.5.1. Validity domains 2.5.2. Topological index 2.5.3. Statistical indices 2.5.3.1. Morisita index 2.5.3.2. K-function 2.5.4. Fractal dimension 2.5.4.1. Sandbox and box-counting fractal dimension 2.5.4.2. Lacunarity 2.6. Conclusion 2.7. References Chapter 3. Geostatistics: Spatial Predictions and Simulations E. SAVELIEVA, V. DEMYANOV and M. MAIGNAN 3.1. Assumptions of geostatistics 3.2. Family of kriging models 3.2.1. Simple kriging 3.2.2. Ordinary kriging 3.2.3. Basic features of kriging estimation 3.2.4. Universal kriging (kriging with trend) 3.2.5. Lognormal kriging 3.3. Family of co-kriging models 3.3.1. Kriging with linear regression 3.3.2. Kriging with external drift 3.3.3. Co-kriging 3.3.4. Collocated co-kriging 3.3.5. Co-kriging application example 3.4. Probability mapping with indicator kriging 3.4.1. Indicator coding 3.4.2. Indicator kriging 3.4.3. Indicator kriging applications 3.4.3.1. Indicator kriging for 241Am analysis 3.4.3.2. Indicator kriging for aquifer layer zonation 3.4.3.3. Indicator kriging for localization of crab crowds 3.5. Description of spatial uncertainty with conditional stochastic simulations 3.5.1. Simulation vs. estimation 3.5.2. Stochastic simulation algorithms 3.5.3. Sequential Gaussian simulation 3.5.4. Sequential indicator simulations 3.5.5. Co-simulations of correlated variables 3.6. References Chapter 4. Spatial Data Analysis and Mapping Using Machine Learning Algorithms F. RATLE, A. POZDNOUKHOV, V. DEMYANOV, V. TIMONIN and E. SAVELIEVA 4.1. Introduction 4.2. Machine learning: an overview 4.2.1. The three learning problems 4.2.2. Approaches to learning from data 4.2.3. Feature selection 4.2.4. Model selection 4.2.5. Dealing with uncertainties 4.3. Nearest neighbor methods 4.4. Artificial neural network algorithms 4.4.1. Multi-layer perceptron neural network 4.4.2. General Regression Neural Networks 4.4.3. Probabilistic Neural Networks 4.4.4. Self-organizing (Kohonen) maps 4.5. Statistical learning theory for spatial data: concepts and examples 4.5.1. VC dimension and structural risk minimization 4.5.2. Kernels 4.5.3. Support vector machines 4.5.4. Support vector regression 4.5.5. Unsupervised techniques 4.5.5.1. Clustering 4.5.5.2. Nonlinear dimensionality reduction 4.6. Conclusion 4.7. References Chapter 5. Advanced Mapping of Environmental Spatial Data: Case Studies L. FORESTI, A. POZDNOUKHOV, M. KANEVSKI, V. TIMONIN, E. SAVELIEVA, C. KAISER, R. TAPIA and R. PURVES 5.1. Introduction 5.2. Air temperature modeling with machine learning algorithms and geostatistics 5.2.1. Mean monthly temperature 5.2.1.1. Data description 5.2.1.2. Variography 5.2.1.3. Step-by-step modeling using a neural network 5.2.1.4. Overfitting and undertraining 5.2.1.5. Mean monthly air temperature prediction mapping 5.2.2. Instant temperatures with regionalized linear dependencies 5.2.2.1. The Föhn phenomenon 5.2.2.2. Modeling of instant air temperature influenced by Föhn 5.2.3. Instant temperatures with nonlinear dependencies 5.2.3.1. Temperature inversion phenomenon 5.2.3.2. Terrain feature extraction using Support Vector Machines 5.2.3.3. Temperature inversion modeling with MLP 5.3. Modeling of precipitation with machine learning and geostatistics 5.3.1. Mean monthly precipitation 5.3.1.1. Data description 5.3.1.2. Precipitation modeling with MLP 5.3.2. Modeling daily precipitation with MLP 5.3.2.1. Data description 5.3.2.2. Practical issues of MLP modeling 5.3.2.3. The use of elevation and analysis of the results 5.3.3. Hybrid models: NNRK and NNRS 5.3.3.1. Neural network residual kriging 5.3.3.2. Neural network residual simulations 5.3.4. Conclusions 5.4. Automatic mapping and classification of spatial data using machine learning 5.4.1. k-nearest neighbor algorithm 5.4.1.1. Number of neighbors with cross-validation 5.4.2. Automatic mapping of spatial data 5.4.2.1. KNN modeling 5.4.2.2. GRNN modeling 5.4.3. Automatic classification of spatial data 5.4.3.1. KNN classification 5.4.3.2. PNN classification 5.4.3.3. Indicator kriging classification 5.4.4. Automatic mapping – conclusions 5.5. Self-organizing maps for spatial data – case studies 5.5.1. SOM analysis of sediment contamination 5.5.2. Mapping of socio-economic data with SOM 5.6. Indicator kriging and sequential Gaussian simulations for probability mapping. Indoor radon case study 5.6.1. Indoor radon measurements 5.6.2. Probability mapping 5.6.3. Exploratory data analysis 5.6.4. Radon data variography 5.6.4.1. Variogram for indicators 5.6.4.2. Variogram for Nscores 5.6.5. Neighborhood parameters 5.6.6. Prediction and probability maps 5.6.6.1. Probability maps with IK 5.6.6.2. Probability maps with SGS 5.6.7. Analysis and validation of results 5.6.7.1. Influence of the simulation net and the number of neighbors 5.6.7.2. Decision maps and validation of results 5.6.8. Conclusions 5.7. Natural hazards forecasting with support vector machines – case study: snow avalanches 5.7.1. Decision support systems for natural hazards 5.7.2. Reminder on support vector machines 5.7.2.1. Probabilistic interpretation of SVM 5.7.3. Implementing an SVM for avalanche forecasting 5.7.4. Temporal forecasts 5.7.4.1. Feature selection 5.7.4.2. Training the SVM classifier 5.7.4.3. Adapting SVM forecasts for decision support 5.7.5. Extending the SVM to spatial avalanche predictions 5.7.5.1. Data preparation 5.7.5.2. Spatial avalanche forecasting 5.7.6. Conclusions 5.8. Conclusion 5.9. References Chapter 6. Bayesian Maximum Entropy – BME G. CHRISTAKOS 6.1. Conceptual framework 6.2. Technical review of BME 6.2.1. The spatiotemporal continuum 6.2.2. Separable metric structures 6.2.3. Composite metric structures 6.2.4. Fractal metric structures 6.3. Spatiotemporal random field theory 6.3.1. Pragmatic S/TRF tools 6.3.2. Space-time lag dependence: ordinary S/TRF 6.3.3. Fractal S/TRF 6.3.4. Space-time heterogenous dependence: generalized S/TRF 6.4. About BME 6.4.1. The fundamental equations 6.4.2. A methodological outline 6.4.3. Implementation of BME: the SEKS-GUI 6.5. A brief review of applications 6.5.1. Earth and atmospheric sciences 6.5.2. Health, human exposure and epidemiology 6.6. References List of Authors Index

Calculus in Vector Spaces, 2nd Ed - Lawrence J.Corwin

Author

Lawrence J. Corwin
Robert H. Szczarba

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824792794
YOP : 2015

Binding : Hardback
Total Pages : 604
CD : No

About the first edition…. “…a unique book based on the year course taught at Yale University…a mathematically beautiful development of the material.” About the second edition… Addressing linear algebra from the basics to the spectral theorem and examining a host of topics in multivariable calculus, including differentiation, integration, maxima and minima, the inverse and implicit function theorems, and differential forms, this thoroughly revised Second Edition of an invaluable reference/text—widely successful through five printings—continues to provide unified, integrated coverage of the two fields. Demonstrating that mathematics is a noncompartmentalized discipline of interrelated subjects, Calculus in Vector Spaces, Second Edition Introduces the derivative as a linear transformation…presents linear algebra in a concrete context based on complementary ideas in calculus…explains differential forms on Euclidean space permitting Green’s theorem, Gauss’s theorem, and Stokes’s theorem to be understood in a natural setting…gives a new clarification of compactness as defined in terms of coverings and in terms of sequences…supplies a novel treatment of eigenvalues and eigenvectors…and more. Contexts -Some Preliminaries. -Vector Spaces. -The Derivative. -The Structure of Vector Spaces. -Compact and Connected Sets. -The Chain Rule, Higher Derivatives, and Taylor's Theorem. -Linear Transformations and Matrices. -Maxima and Minima. -The Inverse and Implicit Function Theorems. -The Spectral Theorem. -Integration. -Iterated Integrals and the Fubini Theorem. -Line Integrals. - Surface Integrals. -Differential Forms. -Integration of Differential Forms. Appendix 1: The existence of determinants, Appendix 2.: Jordan canonical form, solutions of selected exercises. Solution of Selected Excercises INdex About the Authors Lawrence J. Corwin was Professor of Mathematics at Rutgers University, New Brunswick, New Jersey, until his death in 1992. Previously he was an Assistant Professor at Yale University, New Haven, Connecticut. The coauthor, with Robert H. Szczarba, of the book Multivariable Calculus (Marcel Dekker, Inc.), he was twice a member of the Institute for Advanced Study, Princeton, New Jersey, held a Sloan Foundation Fellowship, and was a member of the American Mathematical Society, the Mathematical Association of America, and the Society for industrial and Applied Mathematics. Dr. Corwin’s research interests focused on harmonic analysis and representation theory for topological groups. He received the M.A. (1965) and Ph.D. (1968) degrees in mathematics from Harvard University, Cambridge, Massachusetts. Robert H. Szczarba is Deputy Provost for Physical Sciences and Engineering and Professor of Mathematics at Yale University, New Haven, Connecticut. A member of the American Mathematical Society and a two-time member of the Institute for Advanced Study, Princeton, New Jersey, he is the coauthor, with Lawrence J. Corwin, of the book Multivariable Calculus (Marcel Dekker, Inc.) and the author of many papers that reflect his research interests in differential and algebraic topology. Dr. Szczarba received the M.S. (1957) and Ph.D. (1960) degrees in mathematics from the University of Chicago, Illinois.

Tensors and the Clifford Algebra - Alphonse Charlier

Author

Alphonse Charlier
Alain Berard
Marie-France Charlier
Daniele Fristot

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824786663
YOP : 2015

Binding : Hardback
Total Pages : 334
CD : No

About the Book… This practical reference/text presents the applications of tensors, Lie groups and algebra to Maxwell, Klein-Gordon and Dirac equations, making elementary theoretical physics comprehensible and high-level theoretical physics accessible.; Providing the fundamental mathematics necessary to understand the applications, Tensors and the Clifford Algebra offers lucid discussions of covariant tensor calculus; examines subjects from a variety of perspectives; supplies highly detailed developments of all calculations; employs the language of physics in its explanations; and illustrates the use of Clifford algebra and tensor calculus in studying bosons and fermions.; and much more! With over 2800 display equations and 14 appendixes, Tensors and the Clifford Algebra is a valuable reference for mathematical physicists and applied mathematicians, and an important text for upper-level undergraduate and graduate students in quantum mechanics, relativity, electromagnetism, theoretical physics, elasticity, and field theory courses. Contents Tensor analysis; Minkowski space; covariant formulation of electromagnetism; the Cayley-Klein parameters; vector algebra; application of Clifford algebra to bosons - Klein-Gordon equation; fermions - Dirac equation. Bibliography, Index About the Authors Alphonse Charlier is Professor of Theoretical Physics and Head of the Solid Physics Laboratory, University of Metz, France. He received the Ph.D.degree (1965) in physics from Louis Pasteur University, Strasbourg, France. Alain Berard is Conference Chair in Theoretical Physics in the Department of Physics, University of Metz, France. He received the These de III-Cycle degree (1976) in elementary particle physics from the University of Paris XI, France. Marie-France Charlier is Conference Chair in Mechanics and Quantum Mechanics in the Department of Physics, University of Metz, France. She received the Doctorat de Specialite degree (1970) in solid state physics from Louis Pasteur University, Strasbourg, France. Deniele Fristot is Research Associate in Solid-State Physics at the Solid Physics Laboratory, University of Metz, France. She received the D.E.A. Genie Physique et Mechanique degree (1989) from the University of Metz.

Noncommutative Geometry and Cayley-smooth Orders - Lieven Le Bruyn

Author

Lieven Le Bruyn

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781420064223
YOP : 2015

Binding : Hardback
Total Pages : 588
CD : No

Noncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the étale local structure of such orders as well as their central singularities and finite dimensional representations. After an introduction to partial desingularizations of commutative singularities from noncommutative algebras, the book presents the invariant theoretic description of orders and their centers. It proceeds to introduce étale topology and its use in noncommutative algebra as well as to collect the necessary material on representations of quivers. The subsequent chapters explain the étale local structure of a Cayley-smooth order in a semisimple representation, classify the associated central singularity to smooth equivalence, describe the nullcone of these marked quiver representations, and relate them to the study of all isomorphism classes of n-dimensional representations of a Cayley-smooth order. The final chapters study Quillen-smooth algebras via their finite dimensional representations. Noncommutative Geometry and Cayley-smooth Orders provides a gentle introduction to one of mathematics' and physics' hottest topics. Features • Presents background information on a variety of topics, including invariant theory, algebraic geometry, and central simple algebras • Discusses the use of étale topology in noncommutative algebra, such as Azumaya algebras and algebras via Luna slices • Explores the indecomposable roots of quivers, the determination of dimension vectors of simple representations, and the results on general quiver representations • Contains the main results on Cayley-smooth orders, including semisimple and nilpotent representations • Provides an introduction to the fast developing theory of Quillen-smooth algebras Contents Preface Introduction Noncommutative algebra Noncommutative geometry Noncommutative desingularizations Cayley-Hamilton Algebras Conjugacy classes of matrices Simultaneous conjugacy classes Matrix invariants and necklaces The trace algebra The symmetric group Necklace relations Trace relations Cayley-Hamilton algebras Reconstructing Algebras Representation schemes Some algebraic geometry The Hilbert criterium Semisimple modules Some invariant theory Geometric reconstruction The Gerstenhaber-Hesselink theorem The real moment map Étale Technology Étale topology Central simple algebras Spectral sequences Tsen and Tate fields Coniveau spectral sequence The Artin-Mumford exact sequence Normal spaces Knop-Luna slices Quiver Technology Smoothness Local structure Quiver orders Simple roots Indecomposable roots Canonical decomposition General subrepresentations Semistable representations Semisimple Representations Representation types Cayley-smooth locus Reduction steps Curves and surfaces Complex moment map Preprojective algebras Central smooth locus Central singularities Nilpotent Representations Cornering matrices Optimal corners Hesselink stratification Cornering quiver representations Simultaneous conjugacy classes Representation fibers Brauer-Severi varieties Brauer-Severi fibers Noncommutative Manifolds Formal structure Semi-invariants Universal localization Compact manifolds Differential forms deRham cohomology Symplectic structure Necklace Lie algebras Moduli Spaces Moment maps Dynamical systems Deformed preprojective algebras Hilbert schemes Hyper Kähler structure Calogero particles Coadjoint orbits Adelic Grassmannian References Index Lieven le Bruyn is Professor of Algebra and Geometry at the University of Antwerp, Belgium. Previously, he served as Research Director of the Belgian Science Foundation. Dr. Le Bruyn is a Iaureate of the Belgian Academy of Sciences and winner of the Louis Empain Prize for Mathematics.

Norm Estimations for Operator Valued Functions and Applications - Michael I.Gil

Author

Michael I. Gil

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824796099
YOP : 2015

Binding : Hardback
Total Pages : 366
CD : No

Providing valuable new tools for specialists in functional analysis and stability theory, this state-of-art reference presents a systematic exposition of estimations for norms of operator-valued function and applies the estimates to spectrum perturbations of linear operators and stability theory. Demonstrating a novel approach to spectrum perturbations, Norm Estimations for Operator-Valued Functions and Applications considers a common procedure for the stability analysis of various classes of equations…extends the well-known spectrum perturbation result for self-adjoint operators to quasi-Hermitian operators…examines spectrum perturbations of operators on a tensor product of Hilbert spaces…covers systems of ordinary differential equations…deals with retarded systems…studies the absolute stability of systems of Volterra equations…emphasizes semilinear evolution equations… Norm Estimations for Operator-Valued Functions and Applications is an ideal resource for mathematicians specializing in functional analysis, stability theory, and control systems theory; mathematical biologists; circuit design engineers; and graduate students in these disciplines. Contents MATRIX-VALUED FUNCTIONS FUNCTIONS OF COMPACT OPERATORS FUNCTIONS OF NONSELF-ADJOINT OPERATORS PERTERBATIONS OF FINITE DIMENSIONAL AND COMPACT OPERATORS PERTERBATIONS OF NONCOMPACT OPERATORS PERTERBATIONS OF OPERATORS ON A TENSOR PRODUCT OF HILBERT SPACES STABILITY AND BOUNDEDNESS OF ORDINARY DIFFERENTIAL SYSTEMS STABILITY OF RETARDED SYSTEMS ABSOLUTE STABILITY OF SOLUTIONS OF VOLETTA INTEGRAL EQUATIONS STABILITY OF SEMILINEAR PARABOLIC SYSTEMS STABILITY OF VOLTERRA INTEGRODIFFERENTIAL SYSTEMS AND APPLICATIONS TO VISCOELASTICITY SEMILINEAR BOUNDARY VALUE PROBLEMS LIST OF MAIN SYMBOLS. About the Author Michael I. Gil’ is a Professor at the Institute for Industrial Mathematics, Beersheva, Israel. The author of several professional publications, Dr. Gil’ is a member of the International Federation of Nonlinear Analysis. He received the Ph.D. degreed (1973) in mathematics from Voronezh State University, Russia, and the Doctor of Physical and Mathematical Sciences (fourth) degree (1990) from the Moscow Institute of System research of the former Soviet Union’s Academy of Science (now the Russian Academy of Science), Russia.

Quadratic Irrationals: An Introduction to Classical Number Theory - Franz Halter-Koch

Author

Franz Halter-Koch

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781466591837
YOP : 2015

Binding : Hardback
Total Pages : 432
CD : No

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups. The book highlights the connection between Gauss’s theory of binary forms and the arithmetic of quadratic orders. It collects essential results of the theory that have previously been difficult to access and scattered in the literature, including binary quadratic Diophantine equations and explicit continued fractions, biquadratic class group characters, the divisibility of class numbers by 16, F. Mertens’ proof of Gauss’s duplication theorem, and a theory of binary quadratic forms that departs from the restriction to fundamental discriminants. The book also proves Dirichlet’s theorem on primes in arithmetic progressions, covers Dirichlet’s class number formula, and shows that every primitive binary quadratic form represents infinitely many primes. The necessary fundamentals on algebra and elementary number theory are given in an appendix. Research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature, the notation is far from being standardized, and a unifying approach to the different aspects is lacking. Covering both classical and recent results, this book unifies the theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational. Contents Foreword Introduction and preface to the reader Notations Quadratic Irrationals Quadratic irrationals, quadratic number fields and discriminants The modular group Reduced quadratic irrationals Two short tables of class numbers Continued Fractions General theory of continued fractions Continued fractions of quadratic irrationals I: General theory Continued fractions of quadratic irrationals II: Special types Quadratic Residues and Gauss Sums Elementary theory of power residues Gauss and Jacobi sums The quadratic reciprocity law Sums of two squares Kronecker and quadratic symbols L-Series and Dirichlet’s Prime Number Theorem Preliminaries and some elementary cases Multiplicative functions Dirichlet L-functions and proof of Dirichlet’s theorem Summation of L-series Quadratic Orders Lattices and orders in quadratic number fields Units in quadratic orders Lattices and (invertible) fractional ideals in quadratic orders Structure of ideals in quadratic orders Class groups and class semigroups Ambiguous ideals and ideal classes An application: Some binary Diophantine equations Prime ideals and multiplicative ideal theory Class groups of quadratic orders Binary Quadratic Forms Elementary definitions and equivalence relations Representation of integers Reduction Composition Theory of genera Ternary quadratic forms Sums of squares Cubic and Biquadratic Residues The cubic Jacobi symbol The cubic reciprocity law The biquadratic Jacobi symbol The biquadratic reciprocity law Rational biquadratic reciprocity laws A biquadratic class group character and applications Class Groups The analytic class number formula L-functions of quadratic orders Ambiguous classes and classes of order divisibility by 4 Discriminants with cyclic 2-class group: Divisibility by 8 and 16 Appendix A: Review of Elementary Algebra and Number Theory Appendix B: Some Results from Analysis Bibliography List of Symbols Subject Index

Representation Theory and Higher Algebraic K-Theory - Aderemi Kuku

Author

Aderemi Kuku

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584886037
YOP : 2015

Binding : Hardback
Total Pages : 460
CD : No

Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of group rings more accessible and provides novel techniques for the computations of higher K-theory of finite and some infinite groups. Authored by a premier authority in the field, the book begins with a careful review of classical K-theory, including clear definitions, examples, and important classical results. Emphasizing the practical value of the usually abstract topological constructions, the author systematically discusses higher algebraic K-theory of exact, symmetric monoidal, and Waldhausen categories with applications to orders and group rings and proves numerous results. He also defines profinite higher K- and G-theory of exact categories, orders, and group rings. Providing new insights into classical results and opening avenues for further applications, the book then uses representation-theoretic techniques-especially induction theory-to examine equivariant higher algebraic K-theory, their relative generalizations, and equivariant homology theories for discrete group actions. The final chapter unifies Farrell and Baum-Connes isomorphism conjectures through Davis-Lück assembly maps. Features • Explores connections between CG and higher algebraic K-theory of C for suitable categories, such as exact, symmetric monoidal, and Waldhausen • Collects computational methods of higher K-theory of noncommutative rings, such as orders and group rings • Describes all higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations for finite, profinite, and compact Lie group actions • Obtains results on higher K-theory of orders ?, and hence group rings, for all n = 0 • Uses certain computations of higher K-theory of orders to produce results on higher K-theory of some infinite groups Contents Introduction REVIEW OF CLASSICAL ALGEBRAIC K-THEORY AND REPRESENTAION THEORY Notes on Notations Category of Representations and Constructions of Grothendieck Groups and Rings Category of representations and G-equivariant categories Grothendieck group associated with a semi-group K0 of symmetric monoidal categories K0 of exact categories - definitions and examples Exercises Some Fundamental Results on K0 of Exact and Abelian Categories with Applications to Orders and Group Rings Some fundamental results on K0 of exact and Abelian categories Some finiteness results on K0 and G0 of orders and groupings Class groups of Dedekind domains, orders, and group rings plus some applications Decomposition of G0 (RG) (G Abelian group) and extensions to some non-Abelian groups Exercises K1, K2 of Orders and Group Rings Definitions and basic properties K1, SK1 of orders and group-rings; Whitehead torsion The functor K2 Exercises Some Exact Sequences; Negative K-Theory Mayer-Vietoris sequences Localization sequences Exact sequence associated to an ideal of a ring Negative K-theory K-n, n positive integer Lower K-theory of group rings of virtually infinite cyclic groups HIGHER ALGEBRAIC K-THEORY AND INTEGRAL REPRESENTATIONS Higher Algebraic K-Theory-Definitions, Constructions, and Relevant Examples The plus construction and higher K-theory of rings Classifying spaces and higher K-theory of exact categories-constructions and examples Higher K-theory of symmetric monoidal categories-definitions and examples Higher K-theory of Waldhausen categories-definitions and examples Exercises Some Fundamental Results and Exact Sequences in Higher K-Theory Some fundamental theorems Localization Fundamental theorem of higher K-theory Some exact sequences in the K-theory of Waldhausen categories Exact sequence associated to an ideal, excision, and Mayer-Vietoris sequences Exercises Some Results on Higher K-Theory of Orders, Group Rings and Modules over "EI" Categories Some finiteness results on Kn, Gn, SKn, SGn of orders and groupings Ranks of Kn(?), Gn(?) of orders and group rings plus some consequences Decomposition of Gn(RG) n = 0, G finite Abelian group; Extensions to some non-Abelian groups, e.g., quaternion and dihedral groups Higher dimensional class groups of orders and group rings Higher K-theory of group rings of virtually infinite cyclic groups Higher K-theory of modules over "EI" -categories Higher K-theory of P(A)G, A maximal orders in division algebras, G finite group Exercises Mod-m and Profinite Higher K-Theory of Exact Categories, Orders, and Groupings Mod-m K-theory of exact categories, rings and orders Profinite K-theory of exact categories, rings and orders Profinite K-theory of p-adic orders and semi-simple algebras Continuous K-theory of p-adic orders MACKEY FUNCTORS, EQUIVARIANT HIGHER ALGEBRAIC K-THEORY, AND EQUIVARIANT HOMOLOGY THEORIES Exercises Mackey, Green, and Burnside Functors Mackey functors Cohomology of Mackey functors Green functors, modules, algebras, and induction theorems Based category and the Burnside functor Induction theorems for Mackey and Green functors Defect basis of Mackey and Green functors Defect basis for KG0 -functors Exercises Equivariant Higher Algebraic K-Theory Together with Relative Generalizations for Finite Group Actions Equivariant higher algebraic K-theory Relative equivariant higher algebraic K-theory Interpretation in terms of group rings Some applications Exercises Equivariant Higher K-Theory for Profinite Group Actions Equivariant higher K-theory (absolute and relative) Cohomology of Mackey functors (for profinite groups) Exercises Equivariant Higher K-Theory for Compact Lie Group Actions Mackey and Green functors on the category A(G) of homogeneous spaces An equivariant higher K-theory for G-actions Induction theory for equivariant higher K-functors Exercise Equivariant Higher K-Theory for Waldhausen Categories Equivariant Waldhausen categories Equivariant higher K-theory constructions for Waldhausen categories Applications to complicial bi-Waldhausen categories Applications to higher K-theory of group rings Exercise Equivariant Homology Theories and Higher K-Theory of Group Rings Classifying space for families and equivariant homology theory Assembly maps and isomorphism conjectures Farrell-Jones conjecture for algebraic K-theory Baum-Connes conjecture Davis-Lück assembly map for BC conjecture and its identification with analytic assembly map Exercise Appendices A: Some computations B: Some open problems References Index

Ordinary Differential Equations - Jane Cronin

Author

Jane Cronin

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824723378
YOP : 2015

Binding : Hardback
Total Pages : 402
CD : No

Requiring only a background in advanced calculus and linear algebra, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations. This third edition of a highly acclaimed textbook provides a detailed account of the Bendixson theory of solutions of two-dimensional nonlinear autonomous equations, which is a classical subject that has become more prominent in recent biological applications. By using the Poincaré method, it gives a unified treatment of the periodic solutions of perturbed equations. This includes the existence and stability of periodic solutions of perturbed nonautonomous and autonomous equations (bifurcation theory). The text shows how topological degree can be applied to extend the results. It also explains that using the averaging method to seek such periodic solutions is a special case of the use of the Poincaré method. Features -Illustrates existence theorems with various examples, such as Volterra equations for predator-prey systems, Hodgkin–Huxley equations for nerve conduction, the Field–Noyes model for the Belousov–Zhabotinsky reaction, and Goodwin equations for a chemical reaction system -Provides a detailed account of the Bendixson theory of solutions of two-dimensional autonomous systems -Presents a unified treatment of the perturbation problem for periodic solutions, covering the Poincaré method, autonomous systems, and bifurcation problems -Shows how topological degree is used to obtain significant extensions of perturbation theory -Describes how the averaging method is used to study periodic solutions Contents Prefaces Introduction Existence Theorems What This Chapter Is About Existence Theorem by Successive Approximations Differentiability Theorem Existence Theorem for Equation with a Parameter Existence Theorem Proved by Using a Contraction Mapping Existence Theorem without Uniqueness Extension Theorems Examples Linear Systems Existence Theorems for Linear Systems Homogeneous Linear Equations: General Theory Homogeneous Linear Equations with Constant Coefficients Homogeneous Linear Equations with Periodic Coefficients: Floquet Theory Inhomogeneous Linear Equations Periodic Solutions of Linear Systems with Periodic Coefficients Sturm–Liouville Theory Autonomous Systems Introduction General Properties of Solutions of Autonomous Systems Orbits near an Equilibrium Point: The Two-Dimensional Case Stability of an Equilibrium Point Orbits near an Equilibrium Point of a Nonlinear System The Poincaré–Bendixson Theorem Application of the Poincaré–Bendixson Theorem Stability Introduction Definition of Stability Examples Stability of Solutions of Linear Systems Stability of Solutions of Nonlinear Systems Some Stability Theory for Autonomous Nonlinear Systems Some Further Remarks Concerning Stability The Lyapunov Second Method Definition of Lyapunov Function Theorems of the Lyapunov Second Method Applications of the Second Method Periodic Solutions Periodic Solutions for Autonomous Systems Stability of the Periodic Solutions Sell’s Theorem Periodic Solutions for Nonautonomous Systems Perturbation Theory: The Poincaré Method Introduction The Case in which the Unperturbed Equation Is Nonautonomous and Has an Isolated Periodic Solution The Case in which the Unperturbed Equation Has a Family of Periodic Solutions: The Malkin–Roseau Theory The Case in which the Unperturbed Equation Is Autonomous Perturbation Theory: Autonomous Systems and Bifurcation Problems Introduction Using the Averaging Method: An Introduction Introduction Periodic Solutions Almost Periodic Solutions Appendix Ascoli’s Theorem Principle of Contraction Mappings The Weierstrass Preparation Theorem Topological Degree References Index

Differential Equations with Maxima - Drumi D.Bainov

Author

Drumi D. Bainov
Snezhana G. Hristova

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781439867570
YOP : 2015

Binding : Hardback
Total Pages : 312
CD : No

Differential equations with "maxima"—differential equations that contain the maximum of the unknown function over a previous interval—adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various technical systems on which our ever-advancing, high-tech world depends. Understanding and manipulating the theoretical results and investigations of differential equations with maxima opens the door to enormous possibilities for applications to real-world processes and phenomena. Presenting the qualitative theory and approximate methods, Differential Equations with Maxima begins with an introduction to the mathematical apparatus of integral inequalities involving maxima of unknown functions. The authors solve various types of linear and nonlinear integral inequalities, study both cases of single and double integral inequalities, and illustrate several direct applications of solved inequalities. They also present general properties of solutions as well as existence results for initial value and boundary value problems. Later chapters offer stability results with definitions of different types of stability with sufficient conditions and include investigations based on appropriate modifications of the Razumikhin technique by applying Lyapunov functions. The text covers the main concepts of oscillation theory and methods applied to initial and boundary value problems, combining the method of lower and upper solutions with appropriate monotone methods and introducing algorithms for constructing sequences of successive approximations. The book concludes with a systematic development of the averaging method for differential equations with maxima as applied to first-order and neutral equations. It also explores different schemes for averaging, partial averaging, partially additive averaging, and partially multiplicative averaging. A solid overview of the field, this book guides theoretical and applied researchers in mathematics toward further investigations and applications of these equations for a more accurate study of real-world problems. Contents Introduction Integral Inequalities with Maxima Linear Integral Inequalities with Maxima for Scalar Functions of One Variable Nonlinear Integral Inequalities with Maxima for Scalar Functions of One Variable Integral Inequalities with Maxima for Scalar Functions of Two Variables Applications of the Integral Inequalities with Maxima General Theory Existence Theory for Initial Value Problems Existence Theory for Boundary Value Problems Differential Equations with "Maxima" via Weakly Picard Operator Theory Stability Theory and Lyapunov Functions Stability and Uniform Stability Integral Stability in Terms of Two Measures Stability and Cone Valued Lyapunov Functions Practical Stability on a Cone Oscillation Theory Differential Equations with "Maxima" versus Differential Equations with Delay Oscillations of Delay Differential Equations with "Maxima" Oscillations of Forced n-th Order Differential Equations with "Maxima" Oscillations and Almost Oscillations of n-th Order Differential Equations with "Maxima" Oscillations of Differential Inequalities with "Maxima" Asymptotic Methods Monotone-Iterative Technique for Initial Value Problems Monotone-Iterative Technique for a Periodic Boundary Value Problem Monotone-Iterative Technique for Second Order Differential Equations with "Maxima" Method of Quasilinearization for an Initial Value Problem Method of Quasilinearization for a Periodic Boundary Value Problem Averaging Method Averaging Method for an Initial Value Problem Averaging Method for Multipoint Boundary Value Problem Partial Averaging Method Partially Additive and Partially Multiplicative Averaging Method Notes and Comments Bibliography

Semigroups - P.A.Grillet

Author

P.A. Grillet

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824796624
YOP : 2015

Binding : Hardback
Total Pages : 410
CD : No

This invaluable, single-source reference/text offers concise coverage of the structure theory of semigroups-thoroughly examining constructions and descriptions of semigroups and emphasizing finite, commutative, regular, and inverse semigroups. Providing a core of classical results, Semigroups introduces, for the first time in a self-contained volume, a host of structure theorems on regular and commutative semigroups...examines associativity and products, homomorphisms, congruences, and free semigroups...discusses Green's relations and the Rees-Sushkevich theorem...describes ideal extensions, semilattice decompositions, subdirect products, and group coextensions ... presents the most important theorems for each area of commutative, finite, regular, and inverse semigroups...furnishes up-to-date analyses of current results in semigroup theory...and much more. Containing key bibliographic citations to facilitate more in-depth study of special topics, Semigroups is a useful reference for pure and applied mathematicians, particularly semigroup theorists and algebraists, as well as computer scientists, and an indispensable text for graduate-level students taking courses in semigroup theory. Contents Semigroups; Green's relations; constructions; commutative semigroups; finite semigroups; regular semigroups; inverse semigroups; fundamental regular semigroups; four classes of regular semigroups. About the Author P. A. GRILLET is a Professor of Mathematics at Tulane University, New Orleans, Louisiana. A member of the American Mathematical Society, he is the author of two monographs and over 60 professional papers that reflect his interest in semigroups and other subjects. Dr. Grillet received the Ph.D. degree (1965) in mathematics from the Universite de Paris (Sorbonne), France.

Theory of Distributions - M.A. Al-Gwaiz

Author

M.A. Al-Gwaiz

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824786724
YOP : 2015

Binding : Hardback
Total Pages : 270
CD : No

This concise reference/text presents a rigorous, motivated introduction to the theory of distributions based on the duality of certain topological vector spaces. Theory of Distributions explicates mathematical structures, including the spaces of distributions and their properties, as well as the Hilbert space aspect of the theory and its applications to typical boundary value problems for second-order linear partial differential equations. Covering all points of the subject, Theory of Distributions discusses locally convex spaces ...distributions of finite order .. . the Fourier transformation .. . and the trace operator in Sobolev space. Aiding classroom work or self-study, this highly readable volume offers over 100 worked-out examples; end-of-chapter problems; over 1500 figures and display equations; a clear, informal presentation; an emphasis on applications; and more! Theory of Distributions is a useful reference for pure and applied mathematicians as well as theoretical physicists, and an excellent textbook for graduate-level students in the theory of distributions and related mathematics and physics courses. Contents Preface, 1. LOCALLY CONVEX SPACES 2. TEST FUNCTIONS AND DISTRIBUTIONS 3. DISTRIBUTIONS WITH COMPACT SUPPORT AND CONVOLUTIONS 4. FOURIER TRANSFORMS AND TEMPERED DISTRIBUTIONS 5. DISTRIBUTIONS IN HILBERT SPACE 6. APPLICATIONS TO BOUNDARY VALUE PROBLEMS NOTATION REFERENCES INDEX About the Author M. A. AL-GWAIZ is an Associate Professor of Mathematics at King Saud University, Riyadh, Saudi Arabia. He is the author of a textbook on complex analysis and of a number of papers which reflect his research interests in boundary value problems for partial di~rential equations, differential geometry, and mathematical physics. Dr. Al-Gwaiz is a member of the American Mathematical Society and the National Society for Mathematics (Saudi Arabia). He received the M .S. degree (1967) in mathematics from the Courant Institute of Mathematical Sciences, New York University, and the Ph.D. degree (1972) in mathematics from the University of Wisconsin - Madison.

Divergence Theorem and Sets of Finite Perimeter - Washek F.Pfeffer

Author

Washek F. Pfeffer

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781466507197
YOP : 2015

Binding : Hardback
Total Pages : 260
CD : No

This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration — no generalized Riemann integrals of Henstock–Kurzweil variety are involved. In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy–Riemann, Laplace, and minimal surface equations. The sets of finite perimeter are introduced in Part II. Both the geometric and analytic points of view are presented. The equivalence of these viewpoints is obtained via the functions of bounded variation. These functions are studied in a self-contained manner with no references to Sobolev’s spaces. The coarea theorem provides a link between the sets of finite perimeter and functions of bounded variation. The general divergence theorem for bounded vector fields is proved in Part III. The proof consists of adapting the combinatorial argument of Part I to sets of finite perimeter. The unbounded vector fields and mean divergence are also discussed. The final chapter contains a characterization of the distributions that are equal to the flux of a continuous vector field. Contents DYADIC FIGURES Preliminaries The setting Topology Measures Hausdorff measures Differentiable and Lipschitz maps Divergence Theorem for Dyadic Figures Differentiable vector fields Dyadic partitions Admissible maps Convergence of dyadic figures Removable Singularities Distributions Differential equations Holomorphic functions Harmonic functions The minimal surface equation Injective limits SETS OF FINITE PERIMETER Perimeter Measure-theoretic concepts Essential boundary Vitali’s covering theorem Density Definition of perimeter Line sections BV Functions Variation Mollification Vector valued measures Weak convergence Properties of BV functions Approximation theorem Coarea theorem Bounded convex domains Inequalities Locally BV Sets Dimension one Besicovitch’s covering theorem The reduced boundary Blow-up Perimeter and variation Properties of BV sets Approximating by figures THE DIVERGENCE THEOREM Bounded Vector Fields Approximating from inside Relative derivatives The critical interior The divergence theorem Lipschitz domains Unbounded Vector Fields Minkowski contents Controlled vector fields Integration by parts Mean Divergence The derivative The critical variation Charges Continuous vector fields Localized topology Locally convex spaces Duality The space BVc(Ω) Streams The Divergence Equation Background Solutions in Lp(Ω; Rn) Continuous solutions Bibliography List of Symbols Index

Unilateral Contact Problems - Christof Eck

Author

Christof Eck
Jiri Jarusek
Miroslav Krbec

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781574446296
YOP : 2015

Binding : Hardback
Total Pages : 416
CD : No

The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics. This book presents the state of the art in the mathematical analysis of unilateral contact problems with friction, along with a major part of the analysis of dynamic contact problems without friction. Much of this monograph emerged from the authors' research activities over the past 10 years and deals with an approach proven fruitful in many situations. Starting from thin estimates of possible solutions, this approach is based on an approximation of the problem and the proof of a moderate partial regularity of the solution to the approximate problem. This in turn makes use of the shift (or translation) technique - an important yet often overlooked tool for contact problems and other nonlinear problems with limited regularity. The authors pay careful attention to quantification and precise results to get optimal bounds in sufficient conditions for existence theorems. Unilateral Contact Problems: Variational Methods and Existence Theorems a valuable resource for scientists involved in the analysis of contact problems and for engineers working on the numerical approximation of contact problems. Self-contained and thoroughly up to date, it presents a complete collection of the available results and techniques for the analysis of unilateral contact problems and builds the background required for further research on more complex problems in this area. Contents PREFACE INTRODUCTION Notations Linear Elasticity Formulation of Contact Problems Variational Principles in Mechanics The Static Contact Problem Geometry of Domains The Method of Tangential Translations BACKGROUND Fixed Point Theorems Some General Remarks Crash Course in Interpolation Besov and Lizorkin-Triebel Spaces The Potential Spaces Vector-Valued Sobolev and Besov Spaces Extensions and Traces Spaces on Domains STATIC AND QUASISTATIC CONTACT PROBLEMS Coercive Static Case Semicoercive Contact Problem Contact Problems for Two Bodies Quasistatic Contact Problem DYNAMIC CONTACT PROBLEMS A Short Survey About Results for Elastic Materials Results for Materials With Singular Memory Viscoelastic Membranes Problems With Given Friction DYNAMIC CONTACT PROBLEMS WITH COULOMB FRICTION Solvability of Frictional Contact Problems Anisotropic Material Isotropic Material Thermo-Viscoelastic Problems BIBLIOGRAPHY LIST OF NOTATION SUBJECT INDEX About the Author Christof Eck is a Lecturer in the Institute of Applied Mathematics, University Erlangen, Germany. Jiri Jarusek and Miroslay Krbec are with the Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague.

Invariant Descriptive Set Theory - Su Gao

Author

Su Gao

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584887935
YOP : 2015

Binding : Hardback
Total Pages : 398
CD : No

Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research. Features • Reviews classical descriptive set theory • Covers all aspects of Polish group actions and equivalence relations • Explores diverse applications in mathematics, including applications to classification problems • Includes a large number of exercises at the end of most sections • Contains an appendix with proofs of useful results about the Gandy–Harrington topology Contents Preface Polish Group Actions Preliminaries Polish spaces The universal Urysohn space Borel sets and Borel functions Standard Borel spaces The effective hierarchy Analytic sets and Σ 1/1 sets Coanalytic sets and π 1/1 sets The Gandy–Harrington topology Polish Groups Metrics on topological groups Polish groups Continuity of homomorphisms The permutation group S∞ Universal Polish groups The Graev metric groups Polish Group Actions Polish G-spaces The Vaught transforms Borel G-spaces Orbit equivalence relations Extensions of Polish group actions The logic actions Finer Polish Topologies Strong Choquet spaces Change of topology Finer topologies on Polish G-spaces Topological realization of Borel G-spaces Theory of Equivalence Relations Borel Reducibility Borel reductions Faithful Borel reductions Perfect set theorems for equivalence relations Smooth equivalence relations The Glimm–Effros Dichotomy The equivalence relation E0 Orbit equivalence relations embedding E0 The Harrington–Kechris–Louveau theorem Consequences of the Glimm–Effros dichotomy Actions of cli Polish groups Countable Borel Equivalence Relations Generalities of countable Borel equivalence relations Hyperfinite equivalence relations Universal countable Borel equivalence relations Amenable groups and amenable equivalence relations Actions of locally compact Polish groups Borel Equivalence Relations Hypersmooth equivalence relations Borel orbit equivalence relations A jump operator for Borel equivalence relations Examples of Fσ equivalence relations Examples of π 0/3 equivalence relations Analytic Equivalence Relations The Burgess trichotomy theorem Definable reductions among analytic equivalence relations Actions of standard Borel groups Wild Polish groups The topological Vaught conjecture Turbulent Actions of Polish Groups Homomorphisms and generic ergodicity Local orbits of Polish group actions Turbulent and generically turbulent actions The Hjorth turbulence theorem Examples of turbulence Orbit equivalence relations and E1 Countable Model Theory Polish Topologies of Infinitary Logic A review of first-order logic Model theory of infinitary logic Invariant Borel classes of countable models Polish topologies generated by countable fragments Atomic models and Gδ-orbits The Scott Analysis Elements of the Scott analysis Borel approximations of isomorphism relations The Scott rank and computable ordinals A topological variation of the Scott analysis Sharp analysis of S∞-orbits Natural Classes of Countable Models Countable graphs Countable trees Countable linear orderings Countable groups Applications to Classification Problems Classification by Example: Polish Metric Spaces Standard Borel structures on hyperspaces Classification versus nonclassification Measurement of complexity Classification notions Summary of Benchmark Equivalence Relations Classification problems up to essential countability A roadmap of Borel equivalence relations Orbit equivalence relations General Σ 1/1 equivalence relations Beyond analyticity Appendix: Proofs about the Gandy–Harrington Topology The Gandy basis theorem The Gandy–Harrington topology on Xlow References Index

Degenerate Differential Equations in Banach Spaces

Author

Angelo Favini
Atsushi Yagi

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824716776
YOP : 2015

Binding : Hardback
Total Pages : 326
CD : No

This innovative reference contains a detailed study of linear abstract degenerate differential equations and the regularity of their relations, using the semigroups generated by multivalued (linear) operators and extensions of the operational method of Da Prato and Grisvard. Degenerate Differential Equations in Banach Spaces establishes the analyticity of the semigroup generated by degenerate parabolic operators in spaces of continuous functions ... studies the maximal regularity in time of solutions to degenerate equations of parabolic type in Banach spaces ... guarantees the existence of "regular" solutions in contrast to the generalized (distributional) solutions appearing in the literature ... introduces the semigroups of weak type generated by multivalued linear operators for the first time ... includes classical results pertaining to linear operators, evolution equations, and interpolation theory ... examines existence theory for the multivalued linear Cauchy problem in the hyperbolic and parabolic cases ... presents recent results on the regularity of semigroups generated by second order degenerate parabolic operators in various function spaces ... and more. With over 1500 references and equations, Degenerate Differential Equations in Banach Spaces is suitable for mathematical analysts, differential geometers, topologists, pure and applied mathematicians, physicists, engineers, and graduate students in these disciplines. Contents PREFACE INTRODUCTION PRELIMINARIES AND NOTATIONS; MULTIVALUED LINEAR OPERATORS; DEGENERATE EQUATIONS OF HYPERBOLIC TYPE; DEGENERATE EQUATIONS OF PARABOLIC TYPE I; DEGENERATE EQUATIONS OF PARABOLIC TYPE II; DEGENERATE EQUATIONS - THE GENERAL CASE; DEGENERATE DIFFERENTIAL EQUATIONS OF THE SECOND ORDER; DEGENERATE PARABOLIC EQUATIONS; BIBLIOGRAPHICAL REMARKS. BIBLIOGRAPHY. LIST OF SYMBOLS. INDEX About the Author ANGELO FAVINI is a Professor in the Department of Mathematics at the University of Bologna, Italy. The author, coauthor, or editor of over 70 research articles and conference proceedings, he is a member of the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni of the Consiglio Nazionale delle Ricerche (Italy). Dr. Favini received the laurea in mathematics (1969) from the University of Bologna, Italy. ARSUSM YAGI is a Professor of Mathematics in the Department of Applied Physics, Osaka University, Japan. A member of the Mathematical Society of Japan, Dr. Yagi received the B.S. degree (1973) in mathematics from Niigata University, Niigata City, Japan, and the M.S. (1975) and Ph.D. (1982) degrees from Osaka University, Japan.

Oscillation Theory for Functional Differential Equations - L.H. Erbe

Author

L.H. Erbe

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824795986
YOP : 2015

Binding : Hardback
Total Pages : 496
CD : No

This valuable reference examines the latest developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, clearly presenting basic oscillation theory as well as up-to-the-minute; results-many previously unpublished. Showing how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations, Oscillalion Theory for Functional Differential Equations explores in detail important topics such as the existence of oscillatory solutions…estimates of the distance between zeros...asymptotic classification of nonoscillatory solutions and criteria for certain types of nonoscillatory solutions...the oscillation of equations with nonlinear neutral terms and the oscillation of systems of equations ... boundary value problems for both singular and nonsingular functional differential equations of second order and equations of nth order ... and more With key bibliographic citations, Oscillalion Theory for Functional Differential Equations is an indispensable resource for pure and applied mathematicians, mathematical analysts, engineers working with differential equations and oscillation theory, and upper-level undergraduate and graduate students in these disciplines. Contents PRELIMINARIES; OSCILLATIONS OF FIRST ORDER DELAY DIFFERENTIAL EQUATIONS; OSCILLATION OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATIONS; OSCILLATION AND NONOSCILLATION OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS; OSCILLATION OF HIGHER ORDER NEUTRAL DIFFERENTIAL EQUATIONS; OSCILLATION OF SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS; BOUNDARY VALUE PROBLEMS FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS.REFERENCES, INDEX L. H. ERBE is Professor in the Mathematics Department at the University of Alberta, Edmonton, Canada. He is the author or coauthor of more than JOO professional papers and book chapters focusing mainly on differential equations and boundary value problems. Dr. Erbe received the Ph.D. degree (1968) in mathematics from the University of Nebraska at Lincoln. QINGKAI KONG is Assistant Professor in the Department of Mathematical Sciences at Northern Illinois University, De Kalb. An invited lecturer at many conferences on the applications of differential equations, he is the author of numerous professional papers in this area. Dr Kong received the Ph.D. degree (1992) in mathematics from the University of Alberta, Edmonton, Canada. B. G. ZHANG is a Professor in the Department of Mathematics at the Ocean University of Qingdao, Shandong, People's Republic of China. The coauthor of four books, including, with G. S. Ladde and V. Lakshmikantham, Oscillation Theory of Differential Equations with Deviating Arguments (Marcel Dekker, Inc.) and over l 00 professional papers focusing mainly on oscillation theory, he is a member of the American Mathematical Society and the Society of Mathematics of China. Dr. Zhang graduated from Shandong University, Jinan, People's Republic of China, in 1957

Real Function Algebras - S.H. Kulkarni

Author

S.H. Kulkarni

Cover Price : Rs 3,995.00

Imprint : CRC Press
ISBN : 9780824786533
YOP : 2015

Binding : Hardback
Total Pages : 194
CD : No

This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography…and more! Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X). With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras. Contents Gleason parts of a real function algebra; boundaries for a real function algebra; isometries of real function algebras; symbols. S. H. KULKARNI is an Assistant Professor in the Department of Mathematics at the Indian Institute of Technology, Madras. The author of more than 25 professional papers, his research interests include functional analysis and numerical analysis, specifically Banach algebras and Fourier transforms. Dr. Kulkarni received the B.Sc. degree (1974) in mathematics from the University of Poona, Pune, India, and the M.Sc. (1976) and Ph.D. (1980) degrees in mathematics from the Indian Institute of Technology, Bombay. B. V. LIMAYE is a Professor in the Department of Mathematics at the Indian Institute of Technology, Bombay. He is the author or editor of five books, and the author of more than 40 professional papers and presentations. His research interests include algebraic analysis and numerical functional analysis, specifically real Banach algebras and the iterative computation of approximate eigenvalues and eigenvectors of differential and integral operators Dr. Limaye received the B.A. degree (1964) in mathematics from the University of Poona, Pune, India, and the A.M. (1966) and Ph.D. (1969) degrees in mathematics from the University of Rochester, New York.

Abstract Algebra: A Comprehensive Treatment - Claudia Menini

Author

Claudia Menini
Freddy Van Oystaeyen

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824709853
YOP : 2015

Binding : Hardback
Total Pages : 764
CD : No

An ambitious, comprehensive book covering subject matter typically taught over the course of two or three years, Abstract Algebra offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to automatically smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe. Including an original treatment of representation of finite groups that avoids the use of semisimple ring theory, Abstract Algebra explains sets, maps, posets, lattices, and other essentials of the algebraic language…Peano’s axioms and cardinality…groupoids, semigroups, monoids, groups… cyclic groups and the symmetric group…Sylow’s theorems…rings, ideals, homomorphisms, and quotient rings…unique factorization and principal ideal and Euclidean domains…quotient fields and the factoriality of rings of polynomials…modules and vector spaces…Galois theory…linear codes…and ordered rings. Contents Preface General Mathematical Concepts Sets Maps Cartesian Product and Binary Relations Posets, Lattices, Zorn's Lemma Peano's Axions Cardinality Quotient Sets Algebraic Structures Groupoids, Semigroups, Monoids Groups The Integers Congruences Normal Subgroups Isomorphism Theorems for Groups Cyclic Groups Direct Product of Groups The Symmetric Group Further Results on Groups Rings, Ideals, and Homomorphisms Quotient Rings Direct Product of Rings Domains, Prime and Maximal Ideals Polynomials UFD, PID and Euclidean Domains The Quotient Field of a Domains Factoriality of Rings of Polynomials Modules and Vector Spaces Field Extensions Galois Extension Finite Fields The Galois Theory of Equations Ruler and compass Constructions Secrets in Finite Fields: Codes Ordered Rings. The Real Numbers Representation of Finite Groups Some Historical Remarks Suggestions for Further Reading Index CLAUDIA MENINI is Professor of Mathematics at the University of Ferrara, Ferrara, Italy. The author or coauthor of over 50 articles and the coeditor of one book, she has more then 15 years’ experience as a full professor. A member of the Unione Matematica Italiana and the American Mathematical Society, Professor Menini received the Doctor in Mathematics degree (1976) from the University of Ferrara, Ferrara, Italy. FREDDY VAN OYSTAEYEN is Professor of Mathematics at the University of Antwerp, UIA, Belgium. The author, coauthor, editor, or coeditor of over 200 articles, proceedings, book chapters, and books, including Algebraic Geometry for Associative Algebras, Brauer Groups and the Cohomology of Graded Rings, Commutative Algebra and Algebraic Geometry, Hopf Algebras and Quantum Groups, Interactions Between Ring Theory and Representations of Algebras, and A Primer of Algebraic Geometry (all titles, Marcel Dekker, Inc.), he is a board member of the Belgium Mathematical Society and a member of the Liaisons Committee of the European Mathematical Society. Professor Van Oystaeyen received the Ph.D. degree (1972) in mathematics from the University of Amsterdam, The Netherlands, and the habilitation (1975) from the University of Antwerp, UIA, Belgium.

Functional Analytic Methods for Partial Differential Equations Hiroki Tanabe

Author

Hiroki Tanabe

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824797744
YOP : 2015

Binding : Hardback
Total Pages : 424
CD : No

Combining both classical and current methods of analysis, this valuable resource presents clear, detailed discussions on the application of functional analytic methods in partial differential equations. Examining evolution equations in Banach spaces, Functional Analytic Methods for Partial Differential Equations furnishes a slightly simplified, self-contained proof of Agmon-Douglis- Nirenberg's LP estimates for boundary value problems...addresses the theory of function spaces, including interpolation inequalities, the Galgliardo-Nirenberg inequality, and Sobolev's imbedding theorems...describes adjoint boundary value problems...offers recent results on parabolic and hyperbolic equations...illustrates the solvability of retarded functional differential equations in Hilbert spaces...gives results on control problems...and much more. Written by a recognized international expert in the field, Functional Analytic Methods for Partial Differential Equations is an important reference for mathematical analysts, geometers, pure and applied mathematicians, physicists, engineers. and graduate-level students in these disciplines. Contents PRELIMINARIES; SINGULAR INTEGRALS; SOBOLEV SPACES; ELLIPTIC BOUNDARY VALUE PROBLEMS; ELLIPTIC BOUNDARY VALUE PROBLEMS (CONTINUED); PARABOLIC EVOLUTION EQUATIONS; HYPERBOLIC EVOLUTION EQUATIONS; RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS; BIBLIOGRAPHICAL REMARKS BIBLIOGRAPHY LIST OF SYMBOLS INDEX HIROKI TAN ABE is a Professor in the Department of Economics at Otemon Gakuin University, Osaka, Japan. The author of three books on functional analysis and evolution equations, he is a member of the Mathematical Society of Japan and the American Mathematical Society Dr. Tanabe received the Ph.D. degree (1960) in mathematics from Osaka University, Japan.

Inequalities for Finite Difference Equations - B.G. Pachpatte

Author

B.G Pachpatte

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824706579
YOP : 2015

Binding : Hardback
Total Pages : 524
CD : No

This reference/text is a treatise on finite difference inequalities that have important applications to theories of various classes of finite difference and sum-difference equations, including several linear and nonlinear finite difference inequalities appearing for the first time in book form-providing a survey of results on fundamental linear and nonlinear finite difference inequalities and applications. Featuring more than 3500 mathematical expressions and over 200 references, Inequalities for Finite Difference Equations introduces a variety of new finite difference inequalities...discusses perturbations...describes applications to various types of finite difference and sum-difference equations...focuses on stability of finite difference systems...considers inequalities involving iterated sums...examines basic multidimensional finite difference inequalities…identifies bounds on the solutions of difference equations...and more. Contents LINEAR FINITE DIFFERENCE INEQUALITIES; NONLINEAR FINITE DIFFERENCE INEQUALITIES I; NONLINEAR FINITE DIFFERENCE INEQUALITIES II; LINEAR MULTIDIMENSIONAL FINITE DIFFERENCE INEQUALITIES; NONLINEAR MULTIDIMENSIONAL FINITE DIFFERENCE INEQUALITIES. REFERENCES AUTHOR INDEX SUBJECT INDEX B. G. PACHPATTE is Professor of Mathematics, Marathwada University, Aurangabad, India. Formerly he was a visiting professor of mathematics under Indo-American Fellowship at the University of Texas at Arlington. A researcher of differential, integral, and difference equations and inequalities, Dr. Pachpatte is the author or coauthor of numerous professional papers and one book, and an associate editor of six international journals. Dr. Pachpatte received the Ph.D. degree (1972) from Marathwada University, Aurangabad, India.

Introduction to Functions of a Complex Variable - J. H. Curtiss

Author

J. H. Curtiss

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824765019
YOP : 2015

Binding : Hardback
Total Pages : 412
CD : No

Introduction to Functions of a Complex Variable provides an introduction to complex analysis at the advanced undergraduate and graduate levels The textbook features a rigorous treatment that should be accessible to those with some knowledge of the structure of the real number system and elementary calculus The book begins at a basic level, and gradually increases in complexity. For example, the Cauchy Integral Theorem-the central contour integration theorem of the subject-is first dealt with in an elementary manner, and then discussed m more detail as the reader' depth of understanding is increased. In early chapters of the book the Cauchy Integral Theorem is proved only for a starlike region. Despite this restricted validation, a large number of the core results of complex function theory can be correctly derived The generalizations of the Cauchy theory to arbitrary closed curves are then taken up; the methods used employ Runge's Theorem on approximation by rational function The emphasis on approximations by rational functions and polynomials-encompassing an early introduction to power series and a later discussion of deep applications of conformal mapping to polynomial approximations- is an important secondary theme not usually found m texts of this kind The several hundred exercises that are also provided make this an outstanding textbook for students of mathematics on the undergraduate and graduate level. Contents FOREWORD PREFACE 1. THE REAL AND COMPLEX NUMBER FIELDS 2. SEQUENCES AND SERIES 3. SEQUENCES AND SERIES OF COMPLEX-VALUE FUNCTIONS 4. INTRODUCTION TO POWER SERIES 5. SOME ELEMENTARY TOPOLOGICAL CONCEPTS 6. COMPLEX DIFFERENTIAL CALCULUS 7. THE EXPONENTIAL AND RELATED FUNCTIONS 8. COMPLEX LINE INTEGRALS 9. INTRODUCTION TO THE CAUCHY THEORY 10. ZEROS AND ISOLATED SINGULARITIES OF ANALYTIC FUNCTIONS 11. RESIDUES AND RATIONAL FUNCTIONS 12. APPROXIMATION OF ANALYTIC FUNCTIONS BY RATIONAL FUNCTIONS, AND GENERALIZATIONS OF THE CAUCHY THEORY 13. CONFORMAL MAPPING SOME NOTATION LISTED BY CHAPTER AND SECTION WHERE THEY FIRST APPEAR REFERENCES INDEX J. H. CURTISS (d. 1977) was Professor Emeritus of Mathematics at the University of Miami, Coral Gables, Florida. He received his Ph D from Harvard University (1935), and taught at Cornell University (1936-1943) and the University of Miami (1959-1975) Dr. Curtiss' research interests included functional approximation on the complex domain, approximations by harmonic polynomials, problems in mathematical statistics, and the theory of numerical analysis. He published more than forty research papers, expository papers, and reviews in the professional literature. He was a fellow of the American Association for the Advancement of Science, a member of the American Mathematical Society, and a fellow of the Institute of Mathematical Statistics. He was Executive Director of the AMS from 1953 to 1959.

Vector and Tensor Analysis, Second Edition - Eutiquio C. Young

Author

Eutiquio C. Young

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824787899
YOP : 2015

Binding : Hardback
Total Pages : 510
CD : No

about the first edition… “…the presentation is very much oriented towards classical elementary physics. The treatment of tensors at this earthy level is unusual but may be just what some students need" – The American Mathematical Monthlv about the second edition... Revised and updated throughout, the Second Edition of Vector and Tensor Analysis presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures and exploring highly complex and technical topics in simplified settings. Maintaining the features that made the first edition so popular, this informative reference/ text incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence, and the curl into the discussion of tensors...combines the test for independence of path and the path independence sections...offers new examples and figures that demonstrate computational methods as well as clarify concepts...introduces subtitles in each section to highlight the appearance of new topics. Provides definitions and theorems in boldface type for easy identification...and more. Contents VECTOR ALGEBRA; DIFFERENTIAL CALCULUS OF VECTOR FUNCTIONS OF ONE VARIABLE; DIFFERENTIAL CALCULUS OF SCALAR AND VECTOR FIELDS; INTEGRAL CALCULUS OF SCALAR AND VECTOR FIELDS; TENSORS IN RECTANGULAR CARTESIAN COORDINATE SYSTEMS; TENSOR IN GENERAL COORDINATES; SOLUTIONS TO SELECTED PROBLEMS. INDEX. EUTIQUIO C. YOUNG is Professor of Mathematics, Florida State University, Tallahassee The author or coauthor of several journal acticles, he is a member of the Mathematical Association of America, Phi Mu Epsilon, and Phi Kappa Phi. Dr. Young received the B.S. degree (1954) in electrical engineering from the Far Eastern University, Manila, Republic of the Philippines, and the M.A. (1960) and Ph.D. (1962) degrees in mathematics from the University of Maryland at College Park.

Plane Algebraic Curves - G. Orzech

Author

G. Orzech
M. Orzech

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824711597
YOP : 2015

Binding : Hardback
Total Pages : 234
CD : No

Plane Algebraic Curves is a classroom-tested textbook for advanced undergraduate and beginning graduate students in mathematics. The book introduces the contemporary notions of algebraic varieties, morphisms of varieties, and adeles to the classical subject of plane curves over algebraically closed fields. By restricting the rigorous development of these notions to a traditional context the book makes its subject accessible without extensive algebraic prerequisites Once the reader's intuition for plane curves has evolved, there is a discussion of how these objects can be generalized to higher dimensional settings. These features, as well as a proof of the Riemann-Roch Theorem based on a combination of geometric and algebraic considerations, make the book a good foundation for more specialized study in algebraic geometry, commutative algebra, and algebraic function fields Plane Algebraic Curves is suitable for readers with a variety of backgrounds and interests The book begins with a chapter outlining prerequisites, and contains informal discussions giving an overview of its material and relating it to non-algebraic topics which would be familiar to the general reader. There is an explanation of why the algebraic genus of a hyperelliptic curve agrees with its geometric genus as a compact Riemann surface, as well as a thorough description of how the classically important elliptic curves can be described in various normal forms. The book concludes with a bibliography which students can incorporate into their further studies. Contents PREFACE CHAPTER 0: PREREQUISITES CHAPTER 1: SOME FACTS ABOUT POLYNOMIALS CHAPTER 2: AFFINE PLANE CURVES CHAPTER 3: TANGENT SPACES CHAPTER 4: THE LOCAL RING AT A POINT CHAPTER 5: PROJECTIVE PLANE CURVES CHAPTER 6: RATIONAL MAPPINGS, BIRATIONAL CORRESPONDENCES AND ISOMORPHISMS OF CURVES CHAPTER 7: EXAMPLES OF RATIONAL CURVES CHAPTER 8: THE CORRESPONDENCE BETWEEN VALUATIONS AND POINTS CHAPTER 9: AN OVERVIEW AND SIDEWAYS GLANCE CHAPTER 10: DIVISORS CHAPTER 11: THE DIVISOR OF A FUNCTION HAS DEGREE 0 CHAPTER 12: RIEMANN’S THEOREM CHAPTER 13: THE GENUS OF A NONSINGULAR PLANE CURVE CHAPTER 14: CURVES OF GENUS 0 AND 1 CHAPTER 15: A CLASSIFICATION OF ISOMORPHISM CLASSES OF CURVES OF GENUS 1 CHAPTER 16: THE GENUS OF A SINGULAR CURVE CHAPTER 17: INFLECTION POINTS ON PLANE CURVES CHAPTER 18: BEZOUT’S THEOREM CHAPTER 19: ADDITION ON A NONSINGULAR CUBIC CHAPTER 20: DERIVATIONS, DIFFERENTIALS AND THE CANONICAL CLASS CHAPTER 21: ADELES AND THE RIEMANN-ROCH THEOREM BIBLIOGRAPHY NOTATION INDEX GRACF ORZECH is Assistant Professor of Mathematics at Queen's University m Kingston. Canada She received her M.A. degree (1965) from Cornell University and her Ph.D. degree (1970) from the University of Illinois at Champaign-Urbana Dr. Orzech is managing editor for the series Queen's Papers in Pure and Applied Mathematics, and she has published two articles on triple cohomology. She is a member of the Mathematical Association of America and the Association for Women in Mathematics. MORRIS ORZECH is Associate Professor of Mathematics at Queen's University in Kingston, Canada He received his Ph.D. degree ( 1967) from Cornell University and was a member of the Institute for Advanced Study at Princeton University (1974-1975). Dr. Orzech's publications include articles about Galois extensions of rings, Brauer groups, and the Hopfian property for rings and modules He is co-author with Charles Small of The Brauer Groups of Commutative Rings (Marcel Dekker, Inc.). Dr. Orzech is a member of the American Mathematical Society.

Coding Theory and Cryptography: The Essentials, Second Edition - D.C. Hankerson

Author

D.C. Hankerson
Gary Hoffman
D.A. Leonard
Charles C Lindner

Cover Price : Rs 3,995.00

Imprint : CRC Press
ISBN : 9780824704650
YOP : 2015

Binding : Hardback
Total Pages : 360
CD : No

about the first edition... "...provides an excellent introduction to the subject at a level that allows all of the important concepts to be developed.” – Zentralblatt fur Mathematik urd ihre Grenzgebiete about the second edition… This highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an easy-to-use manner appropriate for students with only a basic background in mathematics--offering revised and updated material on the Berlekamp-Massey decoding algorithm and convolutional codes. The revised edition includes an extensive new section on cryptography, designed for an introductory course on the subject. Contents Preface Part I: Coding Theory 1. Introduction to Coding Theory 2. Linear Codes 3. Perfect and Related Codes 4. Cyclic Linear Codes 5. BCH Codes 6. Reed-Solomon Codes 7. Burst Error-Correcting Codes 8. Convolutional Codes 9. Reed-Muller and Preparata Codes Part II: Cryptography 10. Classical Cryptography 11. Topics in Algebra and Number Theory 12. Public-key Cryptography A The Euclidean Algorithm B Factorization of 1 + xn C Examples of Compact Disk Encoding D Solutions to Selected Exercises Bibliography Index D. R. HANKERSON is Professor of Mathematics at Auburn University, Alabama. He received the Ph.D. degree (1986) in mathematics from the University of Nebraska at Lincoln. D. G. HOFFMAN is Professor of Mathematics at Auburn University, Alabama. The author or coauthor of over 20 journal articles, he received the Ph.D. degree (1976) in mathematics from the University of Waterloo, Ontario, Canada. D. A. LEONARD is Professor of Mathematics at Auburn University, Alabama. A member of the American Mathematical Society and Institute of Combinatorics and Its Applications, he received the Ph.D. degree (1980) in mathematics from Ohio State University, Columbus. C. C LINDNER is Professor of Mathematics at Auburn University, Alabama. A member of the American Mathematical Society, the Mathematical Association of America, the Combinatorial Mathematics Society of Australasia, and the Canadian Mathematical Society, he received the Ph.D. degree (1969) in mathematics from Emory University, Atlanta, Georgia. K. T. PHELPS is Professor of Mathematics at Auburn University, Alabama. A member of the Society for Industrial and Applied Mathematics, he received the Ph.D. degree (1976) in mathematics from Auburn University, Alabama. C. A. RODGER is Professor of Mathematics at Auburn University, Alabama. The author or coauthor of over 110 journal articles and book chapters, he is a Fellow of the Australian Mathematics Society, a Foundation Fellow of the Institute of Combinatorics and Its Applications, and a member of the Combinatorial Mathematics Society of Australasia. Professor Rodger received the Ph.D. degree (1982) in mathematics from the University of Reading, Berkshire, England.

Foundations of Translation Planes - Mauro Biliotti

Author

Mauro Biliotti
Vikram Jha
Norman Johnson

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824706098
YOP : 2015

Binding : Hardback
Total Pages : 558
CD : No

This up-to-the-minute reference/text provides comprehensive coverage of the construction and analysis of translation planes with regard to spreads, partial spreads, coordinate structures, automorphisms, autotopisms, and collineation groups-emphasizing the manipulation of incidence structures by various coordinate systems, including quasifields , spreads , and matrix spreadsets . Containing geometric, algebraic, and group-theoretic approaches to translation planes. as well as numerous problem/solution exercises ,Foundations of Translation Planes discusses the theory of coordinatization...tangentially transitive translation planes...the theorems of Ostrom, Hering, Foulser, and Andre...fundamental analysis of matrix spread sets...and more. CONTENTS PREFACE; AN OVERVIEW;ANDRE'S THEORY OF SPREADS; SPREADS IN PG(3,K); PARTIAL SPREADS AND TRANSL ATION NETS; SPREADSHEETS AND PARTIAL SPREADSETS; GEOMETRY OF SPREADSETS; CO-ORDINATIZATION BY SPREADSETS - GENERAL CASES; PARTIAL QUASIFIELDS; CO-ORDINATIZATION BY (PARTIAL) QUASIFIELDS; RATIONAL DESARGUESIAN NETS; QUASIGROUPS, LOOPS AND NUCLEI; (PRE)QUASIFIELDS -ALGEBRAIC AXIOMS AND AUTOPISMS; THE KERNEL OF SPREADSETS AND QUASIFIELDS; QUADRATICS OF TWO DIMENSIONAL QUASIFIELDS - HALL SYSTEMS; SPREADS IN PROJECTIVE SPACES; KERNEL SUBPLANES ACROSS DESARGUESIAN NETS; DERIVATION OF FINITE SPREADS; FOULSER'S COVERING THEOREM; STRUCTURE OF BAER GROUPS; FROBENIUS COMPLEMENTS, P-PRIMITIVE COLLINEATIONS, AND KLEIN-4 GROUPS; LARGE PLANAR GROUPS; FINITE GENERALIZED ANDRE SYSTEMS AND NEARFIELDS; ELATION NET THEORY; BAER-ELATION THEORY; SIMPLE T-EXTENSIONS OF DERIVABLE NETS; CYCLIC SEMIFIELDS; BAER GROUPS ON PARABOLIC SPREADS; LIFTING AND QUASIFIBRATIONS; MIXED TANGENTIALLY TRANSITIVE PLANES; MAXIMAL PARTIAL SPREADS; FOULSER-JOHNSON SL (2,Q)-THEOREM; APPENDICES; BIBLIOGRAPHY;INDEX MAURO BILIOTTI is Professore Ordinario di Geometria Superiore at the University of Lecce, Italy. The author or coauthor of numerous publications, he serves on the Editorial Board of Note di Matematica. A contributing author to Mostly Finite Geometries, edited by Norman L. Johnson (Marcel Dekker, Inc.), he received the Professore Straordinario di Geometria Superiore (1981) and the Professore Ordinario di Geometria Superiore (1984) at the University of Lecce,Italy. VIKRAM JHA is a Reader in the Mathematics Department of Glasgow Caledonian University, Scotland. The author or coauthor of over 60 research articles on translation planes and related areas of finite geometries and nonassociative algebras, he is a member of the Institute of Combinatorics and Its Applications. A contributing author to Mostly Finite Geometries, edited by Norman L. Johnson (Marcel Dekker, Inc.), he received the PhD. degree (1972) from Queen Mary and Westfield College, University of London, England. NORMAN L. JOHNSON is a Professor of Mathematics at the University of Iowa, Iowa City. The author or coauthor of over 200 books and research articles and an Editor of Note di Matematica, he is the author, coauthor, or coeditor of Finite Geometries, Mostly Finite Geometries, and Subplane Covered Nets (all titles, Marcel Dekker, Inc.) and a referee for numerous journals, the National Science Foundation, the National Security Association, and the Research Councils of Canada and CONICET. He received the BA. degree (1964) from Portland State University, Oregon, and the MA. (1966) and PhD. (1968) degrees from Washington State University, Pullman.

Compatibility, Stability, and Sheaves - J.L. Bueso

Author

J.L. Bueso
P. Jara
A. Verschoren

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824795894
YOP : 2015

Binding : Hardback
Total Pages : 280
CD : No

This unique. self-contained reference-the first in-depth examination of compatibility of its kind-integrates fundamental techniques from algebraic geometry, localization theory, and ring theory and demonstrates how each of these topics is enhanced by interaction with the others, providing new results within a common framework Connecting classical theory and novel methods, Compatibility, Stability, and Sheaves furnishes clear presentations of technical conclusions illustrated with concrete examples…supplies all necessary background information on abstract localization theory…highlights the second layer condition...describes basic sheaf constructions over arbitrary rings…studies in detail different types of ring extensions, concentrating on features related to the behavior of prime ideals and localization...investigates the Artin-Rees property and its variants in the noncommutative case and shows how they are related…discusses structure sheaves, including the compatibility results needed to understand their construction and functorial behavior…and more. Written by three of the world's acknowledged experts in the field, Compatibility, Stability, and Sheaves 1s an excellent resource for algebraists, number, ring, category, and K-theorists, pure and applied mathematicians; geometers and algebraic geometers; topologists; mathematical analysts working with sheaves or localization; and graduate-level students in these disciplines. CONTENTS LOCALIZATION; EXTENSIONS; STABILITY; COMPATIBILITY AND SHEAVES; BIBLIOGRAPHY; INDEX J L BUESO is a Professor m the Department of Algebra at the University of Granada, Spam. The author or editor of four books and some 30 professional papers, he is the organizer of several meetings in ring theory and its applications Dr Bueso received the Ph.D degree (1980) in mathematics from the University of Granada, Spain. P JARA 1s a Professor in the Department of Algebra at the University of Granada, Spain. A member of the American Mathematical Society and the Real Sociedad Matematica Espanola, he is the author or editor of three books and the author of over 25 professional papers Dr. Jara received the Ph. D degree (1983) in mathematics from the Umversuy of Granada, Spain. A VERSCHOREN is a Professor of Geometry at the University of Antwerp, Belgium. He is the author, coauthor, or coeditor of 11 books. including Reflectors and Localization Application to Sheaf Theory, Relative Invariants of Rings• The Commutative Theory. Relative Invariants of Rings: The Noncommutative Theory, all with F. Van Oystaeyen, and Relative Invariants of Sheaves (all titles, Marcel Dekker, Inc ) In addition, he is the author or coauthor of over 100 professional papers and a member of the American Mathematical Society, the Belgian Mathematical Society, and the European Mathematical Society. A Laureate of the Belgian Academy of Sciences, Professor Verschoren received the Ph. D degree (1979) in algebraic geometry from the University of Antwerp. Belgium.

Linear and Integer Programming: Theory and Practice, Second Edition - Gerard Sierksma

Author

Gerard Sierksma

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824706739
YOP : 2015

Binding : Hardback
Total Pages : 650
CD : No

about the first edition... " ... this book is well-suited to accompany courses in operations research .... mathematical theory is well motivated by interesting and plausible examples." -Mathematical Reviews about the second edition... This authoritative reference/text combines the theoretical and practical aspects of linear and integer programming-providing practical case studies and techniques, including rounding-off, column-generation, game theory, multiobjective optimization, and goal programming as well as real-world solutions to the transportation and transshipment problem, project scheduling, decentralization, and machine scheduling problems. Thoroughly reorganized throughout to provide enhanced logical and clear presentation of the topics discussed, linear and Integer Programming, Second Edition decouples theory and solutions for in-depth analyses ... covers duality, degeneracy, and multiplicity from a geometrical viewpoint...considers branch-and-bound, simplex, revised simplex, and network simplex techniques...examines sensitivity analysis ... details the Gilmore-Gomory and Bender decomposition methods...highlights the interior path version of Karmarkar's method ... examines mixed-integer programming and the theory of logical variables ... demonstrates the theory of totally unimodular and network matrices ... outlines linear algebra, convexity, and graph theory...displays flow diagrams for composing courses .. contains software for the interior path method...and more. CONTENTS LINEAR OPTIMISATION; BASIC CONCEPTS; DANTZIG'S SIMPLEX METHOD; DUALITY AND OPTIMALITY; SENSITIVITY ANALYSIS; KARMARKAR'S INTERIOR PATH METHOD; INTEGER LINEAR PROGRAMMING; LINEAR NETWORK MODELS; COMPUTATIONAL COMPLEXITY ISSUES; MODEL BUILDING, CASE STUDIES, AND ADVANCED TECHNIQUES; SOLUTIONS TO SELECTED EXERCISES. APPENDICES: LINEAR ALGEBRA; CONVEXITY; GRAPH THEORY; COMPUTER PACKAGE INTPM. BIBLIOGRAPHY; LIST OF SYMBOLS;INDEX GERARD SIERKSMA is a Professor of Logistical Management and Operations Research at the University of Groningen, The Netherlands. The author or coauthor of numerous professional publications, ranging from pure mathematics and philosophy to logistics and sports, Dr. Sierksma 1s a Fellow of the Canadian Institute of Combinatorics and Its Applications and a member of the American Institute for Operations Research and Management Sciences, the Netherlands Society for Statistics and Operations Research, and the Dutch Mathematical Society. He received the M.Sc. degree (1970) in mathematics and physics and the Ph.D. degree (1976) in mathematics from the University of Groningen, The Netherlands.

Differential Geometry and Relativity Theory - Richard L. Faber

Author

Richard L. Faber

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824717490
YOP : 2015

Binding : Hardback
Total Pages : 266
CD : No

Differential Geometry and Relativity Theory: An Introduction approaches relativity as a geometric theory of space and time in which gravity is a manifestation of space-time curvature, rather than a force. Uniting differential geometry and both special and general relativity in a single source, this easy-to-understand text opens the general theory of relativity to mathematics majors having a background only in multivariable calculus and linear algebra. The book offers a broad overview of the physical foundations and mathematical details of relativity, and presents concrete physical interpretations of numerous abstract concepts in Riemannian geometry. The work is profusely illustrated with diagrams aiding in the understanding of proofs and explanations. Appendices feature important material on vector analysis and hyperbolic functions. Differential Geometry and Relativity Theory: An Introduction serves as the ideal text for high-level undergraduate courses in mathematics and physics, and includes a solutions manual augmenting classroom study. It is an invaluable reference for mathematicians interested in differential and Riemannian geometry, or the special and general theories of relativity. Contents PREFACE ACKNOWLEDGMENTS I SURFACES AND THE CONCEPT OF CURVATURE - Curves - Gauss Curvature (Informal Treatment) - Surfaces in E3 - The First Fundamentals Form - The Second Fundamental Form - The Gauss Curvature in Detail - Geodesics - The Curvature Tensor and the Theorema Egregium - Manifolds II SPECIAL RELATIVITY (THE GEOMETRY OF FLAT SPACETIME) - Inertial Frames of Reference - The Michelson-Morley Experiment - The Postulates of Relativity - Relativity of Simultaneity - Coordinates - Invariance of the Interval - The Lorentz Transformation - Spacetime Diagrams - Lorentz Geometry - The Twin Paradox - Temporal Order and Causality III GENERAL RELATIVITY (THE GEOMETRY OF CURVED SPACETIME) - The Principles of Equivalence - Gravity as Spacetime Curvature - The Consequence’s of Einstein’s Theory - The Universal Law of Gravitation - Orbit’s in Newton’s Theory - Geodesics - The Field Equations - The Schwarzschild Solution - Orbits in General Relativity - The Bending of Light APPENDIX A - Vector Geometry and Analysis APPENDIX B – Hyperbolic Functions BIBLIOGRAPHY INDEX RICHARD L. FABER is Associate Professor of Mathematics at Boston College, Chestnut Hill, Massachusetts–a position he has held since 1971. He received the B.S. degree (1960) from Massachusetts Institute of Technology, and the M.A. and Ph.D degrees (1962, 1965 respectively) from Brandeis University, Waltham, Massachusetts. Dr. Faber's research interests include computer science, non-Euclidean geometry, differential geometry, history of geometry, and general relativity, and he has published a number of papers in these areas. He is the author of Foundations of Euclidean and Non-Euclidean Geometry (Marcel Dekker, Inc.).

Advanced Calculus - William L.Voxman

Author

William L. Voxman
Roy H. Goetschel

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824769499
YOP : 2015

Binding : Hardback
Total Pages : 690
CD : No

Advanced Calculus An Introduction to Modem Analysis, an advanced undergraduate textbook, provides mathematics majors, as well as students who need mathematics In their field of study, with an introduction to the theory and applications of elementary analysis. The text presents, in an accessible form, a carefully maintained balance between abstract concepts and applied results of significance that serves to bridge the gap between the two- or three-semester calculus sequence and senior/graduate level courses in the theory and applications of ordinary and partial differential equations, complex variables, numerical methods, and measure and integration theory. The book focuses on topological concepts, such u compactness, connectedness, and metric spaces, and topics from analysis including Fourier series, numerical analysis, complex integration, generalized functions, and Fourier and Laplace transforms. Applications from genetics, spring systems, enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, and brachistochrone problems illustrate this book's usefulness to the non-mathematics major. Extensive problem sets found throughout the book test the student's understanding of the topics and help develop the student's ability to handle more abstract mathematical ideas. Advanced Calculus: An Introduction to Modem Analysis is intended for junior• and senior-level undergraduate students in mathematics, biology, engineering, physics, and other related disciplines An excellent textbook for a one-year course In advanced calculus, the methods employed in this text will increase students' mathematical maturity and prepare them solidly for senior/graduate level topics. The wealth of materials in the text allows the instructor to select topics that are of special interest to the student A two- or three-semester calculus sequence is required for successful use of this book. Contents Preface Chapter 1: Preliminaries Chapter 2: Introduction to Linear Algebra and Ordinary Differential Equations Chapter 3: Limits and Metric Spaces Chapter 4: Continuity, Compactness, and Connectedness Chapter 5: The Derivation: Theory and Elementary Applications Chapter 6: A first Look at Integration Chapter 7: Differentiation of Functions of Several Variables Chapter 8: Sequences and Series Chapter 9: Elementary Applications of Infinite Series Chapter 10: An Introduction to Fourier Analysis Chapter 11: An Introduction to Modern Integration Theory Chapter 12: An Introduction to Complex Integration Chapter 13: The Fourier and Laplace Transforms Chapter 14: A Sampling of Numerical Analysis Answers to Selected Problems Appendix: Table of Laplace Transforms Symbols Used in the Text Index WILLIAM L. VOXMAN is Professor of Mathematics at the University of Idaho, Moscow. Dr. Voxman received his B.A. (1960), M.S. (1963) and PhD. degrees (1968) from the University of Iowa. He has taught in Chile and Ecuador on Latin American Teaching Fellowships and Fullbright Travel Grants, and co-authored a book with Charles O. Christenson, Aspects of Topology (Marcel Dekker, Inc.). A member of Sigma Xi and the American Mathematical Society, Dr. Voxman's research interests are general topology, mathematical applications to biology, and fuzzy sets and systems. ROY H. GOETSCHEL, JR. is Associate Professor of Mathematics at the University of Idaho, Moscow. Dr. Goetschel received his PhD. degree (1966) from the University of Wisconsin, and he taught at Sonoma State College from 1966 to 1969 before joining the University of Idaho faculty in 1969. Dr. Goetachel's research interests include asymptotic methods, turning point problems in differential equations, and fuzzy set theory.

Classes of Modules - John Dauns

Author

John Dauns
Yiqiang Zhou

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584886600
YOP : 2015

Binding : Hardback
Total Pages : 228
CD : No

By working with natural classes and type submodules (TS), Classes of Modules demonstrates the importance of the next generation of ring and module theory. It shows how to achieve positive results by placing restrictive hypotheses on only a small subset of the complement submodules, i.e., the TS. Furthermore, it explains why direct sum decompositions of various kinds exist. Carefully developing the foundations of the subject, the authors begin by providing background on the terminology and introducing the different module classes. The modules classes consist of torsion, torsion-free, s[M], natural, and prenatural. They expand the discussion by exploring advanced theorems and new classes, such as new chain conditions, TS-module theory, and the lattice of prenatural classes of right R-modules. The book finishes with a study of the lattice of prenatural classes and its Boolean sublattice of natural classes. Through the novel concepts presented, Classes of Modules provides a new, unexplored direction to take in ring and module theory. Features • Explores the themes of natural classes and TS, and how they structure much of ring and module theory • Gives tools, new methods, and new concepts to advance ring and module research • Compiles previously scattered material with improved and expanded results as well as simplified proofs • Offers new proofs and explanations that cannot be found in other literature • Provides self-contained, accessible material for those with some knowledge of basic ring theory Contents Preface Note to the Reader List of Symbols PRELIMINARY BACKGROUND Notation and Terminology Lattices IMPORTANT MODULE CLASSES AND CONSTRUCTIONS Torsion Theory The Module Class s[M] Natural Classes M-Natural Classes Pre-Natural Classes FINITENESS CONDITIONS Ascending Chain Conditions Descending Chain Conditions Covers and Ascending Chain Conditions TYPE THEORY OF MODULES: DIMENSION Type Submodules and Type Dimensions Several Type Dimension Formulas Some Non-Classical Finiteness Conditions TYPE THEORY OF MODULES: DECOMPOSITIONS Type Direct Sum Decompositions Decomposability of Modules Unique Type Closure Modules TS-Modules LATTICES OF MODULE CLASSES The Lattice of Pre-Natural Classes More Sublattice Structures Lattice Properties of Npr (R) More Lattice Properties of Npr (R) The Lattice Nr(R) and Its Applications The Boolean Ideal Lattice REFERENCES INDEX John Dauns is a member of the American Mathematical Society and a professor of mathematics at Tulane University, New Orleans, Louisiana, USA. Yiqiang Zhou is a member of the Canadian Mathematical Society and an associate professor of mathematics at Memorial University of Newfoundland, St. John’s, Canada.

Direct Sum Decompositions of Torsion Free Finite Rank Groups - Theodore G.Faticoni

Author

Theodore G. Faticoni

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9781584887263
YOP : 2015

Binding : Hardback
Total Pages : 338
CD : No

With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups. Offering a unified approach to theoretic concepts, this reference covers isomorphism, endomorphism, refinement, the Baer splitting property, Gabriel filters, and endomorphism modules. It shows how to effectively study a group G by considering finitely generated projective right End(G)-modules, the left End(G)-module G, and the ring E(G) = End(G)/N(End(G)). For instance, one of the naturally occurring properties considered is when E(G) is a commutative ring. Modern algebraic number theory provides results concerning the isomorphism of locally isomorphic rtffr groups, finitely faithful S-groups that are J-groups, and each rtffr L-group that is a J-group. Features • Uses modern algebraic number theory to answer various questions regarding groups • Discusses direct sum decompositions of rtffr groups using A(.) • Employs the localization theory in S to study E(G) • Examines commutative endomorphism rings of rtffr groups–rings that have often been overlooked in the literature • Characterizes rtffr groups G that satisfy the Baer splitting property • Investigates possible homological dimensions of the left End(G)-module G • Contains useful appendices, motivational examples, and numerous exercises to reinforce the concepts Contents PREFACE NOTATION AND PRELIMINARY RESULTS Abelian Groups Associative Rings Finite Dimensional Q-Algebras Localization in Commutative Rings Local-Global Remainder Integrally Closed Rings Semi-Perfect Rings Exercise MOTIVATION BY EXAMPLE Some Well Behaved Direct Sums Some Badly Behaved Direct Sums Corner's Theorem Arnold-Lady-Murley Theorem Local Isomorphism Exercises Questions for Future Research LOCAL ISOMORPHISM IS ISOMORPHISM Integrally Closed Rings Conductor of an Rtffr Ring Local Correspondence Canonical Decomposition Arnold's Theorem Exercises Questions for Future Research COMMUTING ENGOMORPHISMS Nilpotent Sets Commutative Rtffr Rings E-Properties Square-Free Ranks Refinement and Square-Free Rank Hereditary Endomorphism Rings Exercises Questions for Future Research REFINEMENT REVISITED Counting Isomorphism Classes Integrally Closed Groups Exercises Questions for Future Research BAER SPLITTING PROPERTY Baer's Lemma Splitting of Exact Sequences G-Compressed Projectives Some Examples Exercises Questions for Future Research J-GROUPS, L- GROUPS, AND S- GROUPS Background on Ext Finite Projective Properties Finitely Projective Groups Finitely Faithful S-Groups Isomorphism versus Local Isomorphism Analytic Number Theory Eichler L-Groups Are J-Groups Exercises Questions for Future Research GABRIEL FILTERS Filters of Divisibility Idempotent Ideals Gabriel Filters on Rtffr Rings Gabriel Filters on QEnd(G) Exercises Questions for Future Research ENDOMORPHISM MODULES Additive Structures of Rings E-Properties Homological Dimensions Self-Injective Rings Exercises Questions for Future Research APPENDIX A: Pathological Direct Sums Nonunique Direct Sums APPENDIX B: ACD Groups Example by Corner APPENDIX C: Power Cancellation Failure of Power Cancellation APPENDIX D: Cancellation Failure of Cancellation APPENDIX E: Corner Rings and Modules Topological Preliminaries The Construction of G Endomorphisms of G APPENDIX F: Corner's Theorem Countable Endomorphism Rings APPENDIX G: Torsion Torsion-Free Groups E-Torsion Groups Self-Small Corner Modules APPENDIX H: E-Flat Groups Ubiquity Unfaithful Groups APPENDIX I: Zassenhaus and Butler Statement Proof APPENDIX J: Countable E-Rings Countable Torsion-Free E-Rings APPENDIX K: Dedekind E-Rings Number Theoretic Preliminaries Integrally Closed Rings BIBLIOGRAPHY INDEX Theodore G. Faticoni is a professor in the department of mathematics at Fordham University, Bronx, New York, USA.

Analysis and Approximation of Contact Problems with Adhesion Or Damage - Mircea Sofonea

Author

Mircea Sofonea
, Weimin Han
Meir Shillor

Cover Price : Rs 3,995.00

Imprint : CRC Press
ISBN : 9781584885856
YOP : 2015

Binding : Hardback
Total Pages : 238
CD : No

Research into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor have carefully selected and thoroughly examined several models in Analysis and Approximation of Contact Problems with Adhesion or Damage. The book describes the most recent models of contact processes with adhesion or damage along with their mathematical formulations, variational analysis, and numerical analysis. Following an introduction to modeling, functional and numerical analysis, the book devotes individual chapters to models involving adhesion and material damage, respectively, with each chapter exploring a particular model. For each model, For each model, the authors provide a variational formulation and establish the existence and uniqueness of a weak solution. They study a fully discrete approximation scheme that uses the finite element method to discretize the spatial domain and finite differences for the time derivatives. The final chapter summarizes the results, presents bibliographic comments, and considers future directions in the field. • Provides a unified presentation of new dynamic and quasistatic models for contact with adhesion or material damage • Presents a systematic development of optimal order error estimates for numerical solutions of the contact problems • Demonstrates convergence of the problems with normal compliance to those with the Signorini condition • Offers a self-contained presentation of the results Employing recent results on elliptic and evolutionary variational inequalities, convex analysis, nonlinear equations with monotone operators, and fixed points of operators, Analysis and Approximation of Contact Problems with Adhesion or Damage places these important tools and results at your fingertips in a unified, accessible reference. Contents Preface List of Symbols Modeling and Mathematical Background Basic Equations and Boundary Conditions Physical Setting and Evolution Equations Boundary Conditions Contact Processes with Adhesion Constitutive Equations with Damage Preliminaries on Functional Analysis Function Spaces and Their Properties Elements of Nonlinear Analysis Standard Results on Variational Inequalities and Evolution Equations Elementary Inequalities Preliminaries on Numerical Analysis Finite Difference and Finite Element Discretizations Approximation of Displacements and Velocities Estimates on the Discretization of Adhesion Evolution Estimates on the Discretization of Damage Evolution Estimates on the Discretization of Viscoelastic Constitutive Law Estimates on the Discretization of Viscoplastic Constitutive Law Frictionless Contact Problems with Adhesion Quasistatic Viscoelastic Contact with Adhesion Problem Statement Existence and uniqueness Continuous Dependence on the Data Spatially Semidiscrete Numerical Approximation Fully Discrete Numerical Approximation Dynamic Viscoelastic Contact with Adhesion Problem Statement Existence and Uniqueness Fully Discrete Numerical Approximation Quasistatic Viscoplastic Contact with Adhesion Problem Statement Existence and Uniqueness for the Signorini Problem Numerical Approximation for the Signorini Problem Existence and Uniqueness for the Problem with Normal Compliance Numerical Approximation of the Problem with Normal Compliance Relation between the Signorini and Normal Compliance Problems Contact Problems with Damage Quasistatic Viscoelastic Contact with Damage Problem Statement Existence and Uniqueness Fully Discrete Numerical Approximation Dynamic Viscoelastic Contact with Damage Problem Statement Existence and Uniqueness Fully Discrete Numerical Approximation Quasistatic Viscoplastic Contact with Damage Problem Statement Existence and Uniqueness for the Signorini Problem Numerical Approximation for the Signorini Problem Existence and Uniqueness for the Problem with Normal Compliance Numerical Approximation of the Problem with Normal Compliance Relation between the Signorini and Normal Compliance Problems Notes, Comments, and Conclusions Bibliographical Notes, Problems for Future Research, and Conclusions Bibliographical Notes Problems for Future Research Conclusions References Index Mircea Sofonea is Professor of Mathematics at the Universite de Perpignan, Perpignan, France. Weimin Han is Professor of Mathematics at the University of lowa, lowa City, USA. Meir Shillor is Professor of Mathematical Sciences at Oakland University, Rochester, Michigan, USA.

Linear Models - Brenton R.Clarke

Author

Brenton R. Clarke

Cover Price : Rs 4,495.00

Imprint : Wiley
ISBN : 9788126552900
YOP : 2015

Binding : Hardback
Total Pages : 270
CD : No

Contents Preface. Acknowledgments. Notation. 1. Introduction. 1.1 The Linear Model and Examples. 1.2 What Are the Objectives?. 1.3 Problems. 2. Projection Matrices and Vector Space Theory. 2.1 Basis of a Vector Space. 2.2 Range and Kernel. 2.3 Projections. 2.3.1 Linear Model Application. 2.4 Sums and Differences of Orthogonal Projections. 2.5 Problems. 3. Least Squares Theory. 3.1 The Normal Equations. 3.2 The Gauss-Markov Theorem. 3.3 The Distribution of SΩ. 3.4 Some Simple Significance Tests. 3.5 Prediction Intervals. 3.6 Problems. 4. Distribution Theory. 4.1 Motivation. 4.2 Non-Central X2 and F Distributions. 4.2.1 Non-Central F-Distribution. 4.2.2 Applications to Linear Models. 4.2.3 Some Simple Extensions. 4.3 Problems. 5. Helmert Matrices and Orthogonal Relationships. 5.1 Transformations to Independent Normally Distributed Random Variables. 5.2 The Kronecker Product. 5.3 Orthogonal Components in Two-Way ANOVA: One Observation per Cell. 5.4 Orthogonal Components in Two-Way ANOVA with Replications. 5.5 The Gauss-Markov Theorem Revisited. 5.6 Orthogonal Components for Interaction. 5.6.1 Testing for Interaction: One Observation per Cell. 5.6.2 Example Calculation of Tukey's One's Degree of Freedom Statistic. 5.7 Problems. 6. Further Discussion of ANOVA. 6.1 The Different Representations of Orthogonal Components. 6.2 On the Lack of Orthogonality. 6.3 The Relationship Algebra. 6.4 The Triple Classification. 6.5 Latin Squares. 6.6 2k Factorial Designs. 6.6.1 Yates' Algorithm. 6.7 The Function of Randomization. 6.8 Brief View of Multiple Comparison Techniques. 6.9 Problems. 7. Residual Analysis: Diagnostics and Robustness. 7.1 Design Diagnostics. 7.1.1 Standardized and Studentized Residuals. 7.1.2 Combining Design and Residual Effects on Fit - DFITS. 7.1.3 The Cook-D-Statistic. 7.2 Robust Approaches. 7.2.1 Adaptive Trimmed Likelihood Algorithm. 7.3 Problems. 8. Models That Include Variance Components. 8.1 The One-Way Random Effects Model. 8.2 The Mixed Two-Way Model. 8.3 A Split Plot Design. 8.3.1 A Traditional Model. 8.4 Problems. 9. Likelihood Approaches. 9.1 Maximum Likelihood Estimation. 9.2 REML. 9.3 Discussion of Hierarchical Statistical Models. 9.3.1 Hierarchy for the Mixed Model (Assuming Normality). 9.4 Problems. 10. Uncorrelated Residuals Formed from the Linear Model. 10.1 Best Linear Unbiased Error Estimates. 10.2 The Best Linear Unbiased Scalar-Covariance-Matrix Approach. 10.3 Explicit Solution. 10.4 Recursive Residuals. 10.4.1 Recursive Residuals and their Properties. 10.5 Uncorrelated Residuals. 10.5.1 The Main Results. 10.5.2 Final Remarks. 10.6 Problems. 11. Further inferential questions relating to ANOVA. References. Index.

Cogalois Theory - Toma Albu

Author

Toma Albu

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824709495
YOP : 2015

Binding : Hardback
Total Pages : 356
CD : No

This volume offers a systematic, comprehensive investigation of field extensions, finite or not, that possess a Cogalois correspondence. The subject is somewhat dual to the very classical Galois Theory dealing with field extensions possessing a Galois correspondence. Solidly backed by over 250 exercises and an extensive bibliography, this book presents a compact and complete review of basic field theory, considers the Vahlen-Capelli Criterion, investigates the radical, Kneser, strongly Kneser, Cogalois, and G-Cogalois extensions, discusses field extensions that are simultaneously Galois and G-Cogalois, and presents nice applications to elementary field arithmetic. Finite Cogalois theory: preliminaries; Kneser extensions; Cogalois extensions; strong Kneser extensions; Galois G-Cogalois extensions; radical extensions and crossed homomorphisms; examples of G-Cogalois extensions; G-Cogalois extensions andprimitive elements; applications to algebraic number fields; connections with graded algebras and Hopf algebras. Infinite Cogalois Theory: infinite Kneser extensions; infinite G-Cogalois extensions; infinite Kummer theory; infinite Galois theory andPontryagin duality; infinite Galois G-Cogalois extensions. Contents Finite Cogalois theory: preliminaries; Kneser extensions; Cogalois extensions; strong Kneser extensions; Galois G-Cogalois extensions; radical extensions and crossed homomorphisms; examples of G-Cogalois extensions; G-Cogalois extensions andprimitive elements; applications to algebraic number fields; connections with graded algebras and Hopf algebras. Infinite Cogalois Theory: infinite Kneser extensions; infinite G-Cogalois extensions; infinite Kummer theory; infinite Galois theory andPontryagin duality; infinite Galois G-Cogalois extensions. Toma Albu is Professor of Mathematics at Atilim University, Ankara, Turkey, and Bucharest University, Romania. His research interests involve ring theory, module theory, field theory, and algebraic number theory. Dr. Albu has authored or coauthored several books and more than 75 articles appearing in various international journals. He received the M.Sc.(1966) and Ph.D (1971) degrees from Bucharest University, Romania. He was a Humboldt Research Fellow at the Universities of Munich and Dusseldorf. Dr. Albu has also held visiting Professor positions in Osaka, Padua, Milwaukee, Columbus, and Santa Barbara.

Difference Equations with Applications to Queues - David L.Jagerman

Author

David L. Jagerman

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824703882
YOP : 2015

Binding : Hardback
Total Pages : 260
CD : No

"This monograph presents a theory of difference and functional equations with continuous argument based on a generalization of the Riemann integral introduced by N.E. Norlund, allowing differentation with respect to the independent variable and permitting greater flexibility in constructing solutions and approximations- solving the nonlinear first order equation by a variety of methods, including an adaptation of the lie grobner theory. With over 1700 featured mathematical expressions. Difference Equations with Applications to Queues shows that the homogeneous sum admits exponential eigenfunctions with explicitly defined eigenvalues… illustrates the value of representations for practical computations… studies the linear difference equation with polynomial coefficients..obtains a singular perturbation solution for the processor sharing queue….Euler-Maclaurin representation for the Norlund sum to the complex plane…gives a theory of the differential difference equation pioneered by C.Truesdell… covers the Erlang loss model of telephone traffic theory, the Engset model, the M/M/1 queue, and the last-in-first out M/M/1 queue with reneging ….proves Heyman’s theorem and explains Casorati’s determinant… discusses linear transformations that state conditions for convergence of Newton series and Norlund sums…and more. Contents OPERATOR FUNCTIONS; GENERALITIES ON DIFFERENCE EQUATIONS; NORLUND SUM, PART 1; NORLAND SUM, PART II; THE FIRST ORDER DIFFERENCE EQUATION; THE LINEAR EQUATION WITH CONSTANT COEFFICIENTS; LINEAR DIFFERENCE EQUATIONS WITH POLYNOMIAL COEFFICIENTS. REFERENCES, INDEX David L.Jagerman is a Mathematical Consultant at RUTCOR- Rutgers Center for Operations Research, Rutgers University, Piscataway, New Jersey. The author or coauthor of over 50 technical papers, Dr. Jagerman is a senior member of the Institute of Electrical and Electronics Engineers. He received the B.E.E. degree from the Cooper Union for the Advancement of Science and Art, New York, New York, and the M.S. and Ph.D. degrees in mathematics from New York University, New York. He was a distinguished member of the technical staff at Bell Laboratories; professor of mathematics at Fairleigh Dickinson University, Teaneck, New Jersey; and professor of mathematics and later computer science at Stevens Institute of Technology, Hoboken, New Jersey.

Classical Sequences in Banach Spaces - Sylvie Guerre-Delabriere

Author

Sylvie Guerre-Delabriere

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824787233
YOP : 2015

Binding : Hardback
Total Pages : 224
CD : No

This unique reference/text offers in depth coverage of Branch spaces that contain co or lp subspaces, and explains the use of such tools and techniques as Schauder bases, ultrapowers, spreading models, and stable banach spaces. Providing a broad view of the subject and completely proving both well known and the most recent results, Classical Sequences in Banach Spaces furnishes detailed discussions of the questions: does every banach space have a basis?... does every Banach space contain a subspace isomorphic to co or lp for some p e [1, +∞[?... if a Banach space contain co or lp for some p, does it contain it almost isometrically?... does any Banach space X contain a subspace isomorphic to co,l1, or a reflexive space?... is it possible to give a characterization of the set of p’s such that lp embeds in a given Banach space X?... is lp (1≤p<+∞) or co always finitely representable in Banach spaces?...does every Banach space contain an unconditional basic sequences?.... and more! Classical Sequences in Banach Spaces is an excellent reference for pure and applied mathematicians, and an invaluable text for graduate-level students in the geometry of Banach spaces and functional analysis courses. Contents Foreword, Preface, Notation and Conventions, 1. Classical Theorems 2. Ultrapowers and Spreading Models 3. Stable Banach Spaces 4. Subspaces of Lp-Spaces, 1 ≤ p < + ∞, References, Index Sylvie Guerre-Delabriere is Lecturer in Mathematics, University of Paris VI, France, A member of the Mathematical Society of France, she is the author of numerous professional papers on the theory of Banach spaces. Dr. Guerre-Delabriere received the Ph.D. degree (1978) in mathematics from the University of Paris VII, and a higher doctorate, the Doctorates Science (1987) in mathematics from the University of Paris VI.

Binary Polynomial Transporms and Nonlinear Digital Filters - S. Agaian

Author

S. Agaian
J. Astola
K. Egiazarian

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824796426
YOP : 2015

Binding : Hardback
Total Pages : 322
CD : No

This unique reference offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. Binary Polynomial Transforms and Nonlinear Digital Filters introduces the Rademacher logical functions...considers fast algorithms for computing Rademacher and polynomial logical functions...focuses attention on general auto- and cross-correlation functions...analyzes Boolean functions via binary polynomial transforms...studies standard median and order statistic filters...explores the statistical properties of stack filters...and much more. CONTENTS PART 1 BINARY POLYNOMIAL TRANSFORMS: BINARY POLYNOMIAL ARITHMETICAL AND LOGICAL FUNCTIONS AND MATRICES; FAST ALGORITHMS AND COMPLEXITY OF BINARY POLYNOMIAL TRANSFORMS; LOGICAL CORRELATIONS AND BINARY POLYNOMIAL TRANSFORMS. PART 2 BINARY POLYNOMIAL TRANSFORMS AND DIGITAL LOGIC: SPECTRAL METHODS IN ANALYSIS OF BOOLEAN FUNCTIONS; SPECTRAL METHODS IN MINIMIZATION OF BOOLEAN FUNCTIONS. PART 3 APPLICATIONS IN NONLINEAR DIGITAL FILTERING: MEDIAN AND ORDER STATISTIC FILTERS; WEIGHTED ORDER STATISTIC AND STACK FILTERS; STATISTICAL PROPERTIES OF STACK FILTERS INDEX S. Agaian is a Visiting Professor in the Department of Electrical Engineering and Computer Science at Tufts University, Medford, Massachusetts, and Head of the Department of Digital Signal Processing of the Institute of Problems of Informatics and Automation, Armenian Academy of Science, Yerevan, Armenia. Dr.Agaian received the M.sc.degree (1968) in mathematics from Yerevan State University, Armenia, and the Ph.D.degree (1973) in physics and mathematics from the V.A.Steklov Institute of Mathematics, Moscow, Russia. He became a full Professor of the Academy of Sciences of the former Soviet Union the 1986. J.Astola is a Professor of signal Processing and the Head of the Signal Processing Laboratory, Tampere University of Technology, Finland. Dr. Astola received the M.Sc.(1973), the Licentiate (1975), and the Ph.D.(1978) degrees in mathematics from the University of Turku, Finland. K.Egiazarian is a Assistant Professor of Signal Processing at the Signal Processing Laboratory, Tempere University of Technology, Finland. Dr. Egiazarian received the M.Sc.degree (1981) in mathematics from Yerevan State University, Armenia the Ph.D. degree (1986) in physics and mathematics from Moscow M.V. Lomonosov State University, Russia, and the Doctor of Technology degree (1994) in signal processing from Tampere University of Technology, Finland.

Hopf Algebras: An Introduction - Sorin Dascalescu

Author

Sorin Dascalescu
Constantin Nastasescu
Serban Raianu

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824704810
YOP : 2015

Binding : Hardback
Total Pages : 412
CD : No

Addressing a wide array of algebraic properties related to Hopf algebras, this exemplary introductory reference/text eloquently works through and summarizes key topics, theories, and relevant features in the field-utilizing the easy to understand language of category theory and providing exercises, solutions, and bibliographic summaries at the end of each chapter. Covering an extensive range of material with clarity and precision, Hopf Algebras features in depth discussions of basic concepts, classes, and theories for algebras, coalgebras, and comodules… the categories, integrals, actions, and coactions of Hopf algebras… special classes of coalgebras such as semiperfect, co-frobenius, cosemisimple, and pointed coalgebras… different sets of behavior for dual notions of coalgebras and comodule….the Nichols-Zoeller, Taft-Wilson, and Kac-Zhu theorems…and more. Contents ALGEBRAS AND COALGEBRAS; COMODULES; SPECIAL CLASSES OF COALGEBRAS; BIALGEBRAS AND HOPF ALGREBRAS; INTEGRALS; ACTIONS AND COACTIONS; FINITE DIMENSIONAL HOPF ALGEBRAS; THE CATEGORY THEORY LANGUAGE; C-GROUPS AND C-COGROUPS BIBLIOGRAPHY INDEX. Sorin Dascalescu is an Associate Professor at the University of Bucharest, Romania. The author or coauthor of over 40 papers and a member of the American Mathematical Society, he received the Ph.D. degree in mathematics (1992) from the University of Bucharest, Romania. Constantin Nastasescu is a Professor of Mathematics at the University of Buchares, Romana. The author or coauthor of over 100 papers and monographs and a member of the American Mathematical Society, he received the Ph.D. degree in mathematics (1970) from the University of Bucharest, Romania. Serban Raianu is an Associate Professor of Mathematics at the University of Bucharest, Romania. The author or coauthor of numerous papers and a member of the American Mathematical Society, he received the Ph.D.degree in mathematics (1991) from the University of Bucharest, Romania.

Elementary Boundary Value Problems - T.A.Bick

Author

T.A. Bick

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824788995
YOP : 2015

Binding : Hardback
Total Pages : 258
CD : No

This practical textbook elucidates the role of BVPs as models of scientific phenomena, describes traditional methods of solution and summarizes the ideas that come from the solution techniques – revolving around the concept of orthonormal sets of functions as generalizations of the trigonometric functions. Emphasizing the unifying nature of the material, Elementary Boundary Value Problems constructs physical models for both bounded and unbounded domains using rectangular and other co-ordinate systems….develops methods of characteristics, eigenfunction expansions, and transform procedures using the traditional fourier series, D'Alembert's method , and fourier integral transforms; makes explicit connections with linear algebra, analysis, complex variables, set theory, and topology in response to the need to solve BVP's presents illustrative examples in science and engineering….and more. Providing fundamental definitions for students with no prior experience in this topic other than differential equations, Elementary Boundary Value Problems is an informative resource for upper-level undergraduate mathematics, physics and engineering, and students in courses on boundary value problems. Contents BOUNDARY VALUE PROBLEMS AS MODELS; THE METHOD OF CHARACTERISTICS; FOURIER SERIES; LINEAR ALGEBRA AND STURM-LIOUVILLE SYSTEMS; FOURIER TRANSFORMS; APPENDICES - A FOURIER SERIES THEORUM, A FOURIER INTEGRAL THEORUM, PROOFS OF THEORUMS 3.5.2 AND 3.5.3, UNIQUENESS THEORUM FOR SECOND-ORDER KINEAR ODE, ON THE SEROES OF THE BESSEL FUNCTIONS, BIBLIOGRAPHY,INDEX. T.A.Bick is Professor of Mathematics at Union College, Schenectady, New York. The author of one book as well as various publications in the areas of ergodic theory and measure theory, he is a member of the Mathematical Association of America. Professor Bick received the B.S.degree (1958) in mathematics from Union College and the M.S. (1960) and Ph.D. (1964) degrees in mathematics from the University of Rochester.

Radical Theory of Rings - B.J.Gardner

Author

J.W. Gardner
R. Wiegandt

Cover Price : Rs 4,495.00

Imprint : CRC Press
ISBN : 9780824750336
YOP : 2015

Binding : Hardback
Total Pages : 400
CD : No

Assimilating radical theory’s evolution in the decades since that last major work on rings and radicals was published, radical theory of rings distills the most noteworthy present day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions. Deals with distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near – rings. Written in clear algebraic terms by globally acknowledged authorities, Radical Theory of Rings provides a systematic treatment of the theory of kurosh – Amitsur radicals as well as of concrete radicals of associative rings… delves into hereditary, supernilpotent, special, supplementing, normal, subidempotent, and A-radicals…gradually introduces concrete radicals as examples of the general theory- arrives at the study of nil radicals and Jacobson, Brown-Mccoy, Behrens, antisimple, strongly prime, and generalized nil radicals…discusses in detail the Density Theorem, Wedderburn-Artin Theorem…and examines the radicals of matrix and polynomial rings and their connection with Koethe’s Problem. Contents Preface, Interdependence Chart, 1. General Fundamentals 2. The General Theory of Radicals 3. Radical Theory for Associative Rings 4. Concrete Radicals and Structure Theorems 5. Special Features of the General Radical Theory, Refereneces, List of Symbols, List of Standard Conditions, Author Index, Subject Index B.J.GARDNER is a Reader in Mathematics at the University of Tasmania, Hobart, Australia. He has authored one book, edited two volumes of conference proceedings, and written some 90 mathematical papers, mostly on algebraic topics. His research areas include radical theory, ring theory, and other branches of algebra. Dr.Gardner received the B.Sc. (1967) and Ph.D. (1971) degrees from the University of Tasmania, Hobart, Australia. R.WIEGANDT is a Scientific Advisor at the A.Renyi Institute of Mathematics, Hungarian Academy of Science, Budapest. An international expert on rings, radials, and other algebraic topics, he is the author or coauthor of some 150 mathematical publications and has served on the editorial boards of nine international mathematical journals. Dr. Wiegandt received the Candidate of Math. Sci. (1967) and Doctor of Math. Sci. (1975) degrees from the Hungarian Academy of Sciences, Budapest.

Complex Analysis and Geometry - V. Ancona

Author

V Ancona
E Ballico
R.M. Miro-Roig
A Silva

Cover Price : Rs 3,995.00

Imprint : CRC Press
ISBN : 9780582292765
YOP : 2015

Binding : Hardback
Total Pages : 200
CD : No

Based on two conferences held recently in Trento, Italy, sponsored by the Centro Internazionale per la Ricerca Matematica (CIRM), this book contains 13 research papers and 2 survey papers on complex analysis and complex algebraic geometry, The main topics are: Mori theory, polynomial hull vector bundles, q-convexity Lie groups and actions on complex space, hypercomplex structures, pseudoconvex domains, and projective varieties, The papers cover the latest advances in these topics and include several open problems. Readership: Graduate students and researchers in complex analysis and algebraic geometry. Contents Preface Contributors On the Limits of Manifolds with nef Canonical Bundles, M. Andreatta and T. Peternell On the Stability of the Restriction of TPn to Projective Curves, E. Ballico and B. Russo Théorie des (a,b)-Modules II. Extensions, D. Barlet Moduli of Reflexive K3 Surfaces, C. Bartocci, U. Bruzzo, and D. Hernández Ruipérez New Examples of Domains with Non-Injective Proper Holomorphic Self-Maps, F. Berteloot and J. J. Loeb Q-Convexivity. A Survey, M. Coltoiu Commuting maps and Families of Hyperbolic Automorphisms, C. de Fabritiis An Alternative Proof of a Theorem of Boas-Straube-Yu, K. Diederich and G. Herbort Large Polynomial Hulls with No Analytic Structure, J. Duval and N. Levenberg Canonical Connections for Almost-Hypercomplex Structures, P. Gauduchon The Tangent Bundle of P2 Restricted to Plane Curves, G. Hein Quotients with Respects to Holomorphic Actions of Reductive Groups, P. Heinzner and L. Migliorini Adjunction Theory on Terminal Varieties, M. Mella Runge Theorem in Higher Dimensions, V. Vajaitu Only Countably Many Simply-Connected Lie Groups Admit Lattices, J. Winkelmann PITMAN RESEARCH NOTES IN MATHEMATICS SERIES The aim of this series is to disseminate important new material of a specialist nature in economic form It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline. The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by mathematical Reviews. This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph, will also be considered for a place in the series. Normally homogeneous material is required, even if written by more than one author, thus multi-author works will be included provided that there is a strong linking theme or editorial pattern.

Approximation Theory - N.K.Govil

Author

N.K. Govil
R.N. Mohapatra
Z. Nashed
A. Sharma

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824701857
YOP : 2015

Binding : Hardback
Total Pages : 542
CD : No

This truly outstanding work honors A.K. Varma’s indelible contributions to the field of approximation theory with a collection of over 30 carefully selected papers by 45 internationally distinguished mathematicians, reflecting his lifelong passion for investigating subjects such as interpolation by polynomials and splines, quadrature formulae, order of pointwise and uniform approximation of finitely differentiable functions by polynomials, and Bernstein and Markov type inequalities in Lp and uniform metrics. Presenting up-to-date research in a single volume, Approximation Theory covers and astonishing breadth of topics, including Lidstone spline interpolation and its error bounds…linear approximation operators….a new proof of the Markov inequality….reliability theory….frames and Schauder, Riesz, and unconditional bases….Birkhoff interpolation…nonlinear subdivision schemes….convex univalent functions….totally positive bases and subdivision matrices….multivariate splines…..a generalization of inequalities of Chebyshev and Turan….the Marcinkiewiez Zygmund inequality….weighted Lagrange interpolation….generalized extended Chebyshev systems and their linear spans….and more. Contents Foreword E.W. Cheney Preface Contributors Arum Kumar Varma: Some Reminiscences 1. Error Bounds for the Derivatives of Lidstone Interpolation and Application Ravi P. Agarwal Patricia J.Y. Wong 2. Higher Order Univariate Wavelet Type Approximation George A. Anastassiou 3. Modified Weighted (0,2) Interpolation J. Balazs 4. New Approach to Markov Inequality in L(p) Norms Mirostaw Baran 5. A Question in Reliability Theory Franck Beaucoup Laurent Carraro 6. Notes on Miscellaneous Approximation Problems Borislav Bojanov 7. Muntz's Theorem on Compact Subsets of Positive Measure Peter Borwein Tamas Erdelyi 8. Frames and Schauder Bases Peter G. Casazza Ole Christensen 9. Interpolation on Spheres by Positive Definite Functions E.W. Cheney Xingping Sun 10. Nonparametric Density Estimation by Polynomials and by Splines Z. Ciesielski 11. Birkhoff Type Interpolation on Perturbed Roots of Unity M.G. de Bruin A. Sharma J. Szabados 12. Approximation by Entire Functions with Only Real Zeros L.T. Dechevsky D.P. Dryanov Q.I. Rahman 13. Nonlinear Means in Geometric Modeling Michael S. Floater Charles A. Micchelli 14. Nonlinear Stationary Subdivision Michael S. Floater Charles A. Micchelli 15. Convex Univalent Functions and Omitted Values Richard Fournier Jinxi Ma Stephan Ruscheweyh 16. Total Positivity and Total Variation T.N.T. Goodman 17. Inequalities for Maximum Modulus of Rational Functions with Prescribed Poles N.K. Govil R.N. Mohapatra 18. Recent Progress on Multivariate Splines Don Hong 19. Hermite Interpolation on Chebyshev Nodes and Walsh Equiconvergence A. Jakimovski A. Sharma 20. Continuous Functions Which Change Sign Without Properly Crossing the x-Axis Peter D. Johnson, Jr. 21. Some Remarks on Weighted Interpolation Theodore Kilgore 22. A Note on Chebyshev's Inequality Xin 23. Smooth Maclaurin Series Coefficients in Pade and Rational Approximation D. S. Lubinsky 24. On Marcinkiewicz-Zygmund-Type Inequalities H.N. Mhaskar J. Prestin 25. Extermal Problems for Restricted Polynomial Classes in L(r) Norm Gradimir V. Milovanovic 26. New Developments on Turan's Extremal Problems for Polynomials Gradimir V. Milovanovic Themistocles M. Rassias 27. Recent Progress in Multivariate Markov Inequality W. Plesniak 28. Orthogonal Expansion and Variations of Sign of Continuous Functions Gerhard Schmeisser 29. Convolution Properties of Two Classes of Starlike Functions Defined by Differential Inequalities Vikramaditya Singh 30. Weighted Lagrange Interpolation on Generalized Jacobi Nodes P. Vertesi 31. Relative Differentiation, Descartes' Rule of Signs, and the Budan-Fourier Theorem for Markov Systems R.A. Zalik Index N.K.Govil is a Professor of Mathematics at Auburn University, Alabama, He received the Ph.D.degree (1968) in mathematics from the University of Montreal, Canada. R.N.Mohapatra is a Professor of Mathematics at the University of Central Floida, Orlando. He received the Ph.D.degree (1968) in mathematics from the University of Jabalpur, India. Z.Nashed is a Professor of Mathematics as well as Electrical Engineering at the University of Delaware, Newark. He received the Ph.D.degree (1963) in mathematics from the University of Michigan, Ann Arbor. A.Sharma is a Professor Emeritus at the University of Alberta, Edmonton, Canada He received the Ph.D.degree (1951) in mathematics from University of Lucknow, India. J.Szabados is Head of the Department of Analysis at the Mathematical Institute of the Hungarian Academy of Science, Budapest. He received the D.Sc.degree (1976) in mathematics from the Hungarian Academy of Sciences, Budapest.

Algebraic Geometry for Associative Algebras - Freddy Van Oystaeyen

Author

Freddy Van Oystaeyen

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824704247
YOP : 2015

Binding : Hardback
Total Pages : 308
CD : No

This innovative reference/text facilitates the definition of a non commutative topology that makes it possible, for the first time, to construct and underlying space where geometric properties can be phrased and studied-resulting in a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level. Constructing the scheme theory from the interaction between graded and filtered algebras appearing as a general deformation principles among geometries, Algebraic Geometry for Associative Algebras fully introduces noncommutative topology…deformation of structure schemes…new cohomological methods….homological algebra and regularity conditions…divisor theory using noncommutative valuations….reductions of algebras….microlocalization and quantum sections….formal completion along subvarieties….and more. Enriched with numerous examples, Algebraic Geometry for Associative Algebras serves as an important research reference for pure and applied mathematicians, particularly algebraists, number theories, ring theorists, geometers, and topologists, as well as a stimulating text for upper level undergraduate and graduate students in these disciplines. Contents PREFACE INTRODUCTION THE NONCOMMUTATIVE SITE STRUCTURE SHEAVES AND THEIR SECTIONS REGULAR ALGEBRAS VALUATIONS AND DIVISORS COHOMOLOGY THEORIES A FUNCTORIAL APPROACH FORMALIZING THE TOPOLOGY REFERENCES INDEX FREDDY VAN OYSTAEYEN is a Professor of Mathematics at the University of Antwerp, UIA, Belgium. The author, coauthor, editor, or coeditor of over 200 articles, proceedings, book chapters, and books, including Brauer Groups and the Cohomology of Graded Rings, Commutative Algebra and Algebraic Geometry, A Primer of Algebraic Geometry, Hopf Algebras and Quantum Groups, and Interactions Between Ring Theory and Representations of Algebras (all titles, Marcel Dekker, Inc.) he is a board member of the Belgium Mathematical Society and a member of the Liaisons Committee of the European Mathematical Society. Professor Van Oystaeyen received the Ph.D.degree (1972) in mathematics from the free University of Amsterdam, The Netherlands, and the habilitation (1975) from the University of Antwerp, UIA, Belgium.

Abstract Algebra with Applications,Vol.1 - Karlheinz Spindler

Author

Karlheinz Spindler

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824791445
YOP : 2015

Binding : Hardback
Total Pages : 774
CD : No

This outstanding textbook offers a comprehensive self contained presentation of all major topics in abstract algebra and provides an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains. Emphasizing both the conceptual and computational aspects of algebra to aid structural thinking as well as operational skills, Abstract Algebra with Applications (in two volumes) includes thorough discussions of group actions; matrix groups; the correlation between ring theory, number theory, and algebraic geometry; Galois theory’ and the applicability of linear algebra….begins each chapter with an introduction that acts as a guide for the material to come….motivates and prepares students for new ideas with informal remarks, enlightening examples, and illustrations that facilitate understanding….furnishes abundant end of section problems of varying levels of difficulty to help students extend and apply their comprehension of newly learned material….allows teachers to use the text for a variety of different courses by maintaining essentially independent chapters….supplies an appendix that contains prerequisites for set theory and point-set topology and their proofs….and much more! With over 230 drawings and numerous diagrams, tables, and display equations, Abstract Algebra with Applications (in two volumes) is the perfect text for all upper-level undergraduate and graduate algebra and related courses, including Abstract Algebra, Linear Algebra, Galois Theory, Commutative Algebra, and Applications of Algebra. Contents Volume I Vector Spaces -First Introduction: Affine Geometry -Second Introduction: Linear Equations -Vector Spaces -Linear and Affine Mappings -Abstract Affine Geometry -Representations of Linear Mappings by Matrices -Determinants -Volume Functions -Eigenvectors and Eigenvalues -Classification of Endomorphisms Up to Similarity -Tensor Products and Base-Field Extension -Metric Geometry -Euclidean Spaces -Linear Mappings Between Euclidean Spaces -Bilinear Forms -Groups of Automorphisms -Application: Markov Chains -Application: Matrix Calculus and Differential Equations Groups -Introduction: Symmetries of Geometric Figures -Groups Subgroups and Cosets -Symmetric and Alternating Groups -Group Homomorphisms -Normal Subgroups and Factor Groups -Free Groups: Generators and Relations -Group Actions -Group-Theoretical Applications of Group Actions -Nilpotent and Solvable Groups -Topological Methods in Group Theory -Analytical Methods in Group Theory -Groups in Topology Appendix Bibliography Index Volume II Preface Rings And Fields - Introduction: The Art of Doing Arithmetic -Rings and Ring Homomorphisms -Integral Domains and Fields -Polynomial and Power Series Rings -Ideals and Quotient Rings -Ideals in Commutative Rings -Factorization in Integral Domains -Factorization in Polynomial and Power Series Rings -Number-Theoretical Applications of Unique Factorization -Modules Noetherian Rings Field Extensions -Noetherian Rings -Field Extensions -Splitting Fields and Normal Extensions -Separability of Field Extensions -Field Theory and Integral Ring Extensions -Affine Algebras -Ring Theory and Algebraic Geometry -Localization -Factorization of Ideals -Introduction to Galois Theory: Solving Polynomial Equations -The Galois Group of a Field Extension -Algebraic Galois Extensions -The Galois Group of a Polynomial -Roots of Unity and Cyclotomic Polynomials -Pure Equations and Cyclic Extensions -Solvable Equations and Radical Extensions -Epilogue: The Idea of Lie Theory as a Galois Theory for Differential Equations Bibliography Index Karlheinz SPindler works in the Flight Dynamics Department of the European Space Operations Centre, Darmstadt, Germany, Previously, he was a teacher of mathematics at the Technische Hochschule Darmstadt, Germany, and a Visiting Assistant Professor of Mathematics at Louisiana State University, Baton Rouge. Dr. Spindler is the author of several professional papers related to Lie Theory. He received his doctorate (1988) in mathematics from the Technische Hochschule Darmstadt.

Topics on Continua - Sergio Macias

Author

Sergio Macias

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780849337383
YOP : 2015

Binding : Hardback
Total Pages : 374
CD : No

Specialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology. In Topics on Continua, Sergio Macías, one of the field’s leading scholars, presents four of his favorite continuum topics: inverse limits, Jones’s set function T, homogenous continua, and n-fold hyperspaces, and in doing so, presents the most complete set of theorems and proofs ever contained in a single topology volume. Many of the results presented have previously appeared only in research papers, and some appear here for the first time. After building the requisite background and exploring the inverse limits of continua, the discussions focus on Professor Jones's set function T and continua for which T is continuous. An introduction to topological groups and group actions lead to a proof of Effros's Theorem, followed by a presentation of two decomposition theorems. The author then offers an in-depth study of n-fold hyperspaces. This includes their general properties, conditions that allow points of n-fold symmetric products to be arcwise accessible from their complement, points that arcwise disconnect the n-fold hyperspaces, the n-fold hyperspaces of graphs, and theorems relating n-fold hyperspaces and cones. The concluding chapter presents a series of open questions on each topic discussed in the book. With more than a decade of teaching experience, Macías is able to put forth exceptionally cogent discussions that not only give beginning mathematicians a strong grounding in continuum theory, but also form an authoritative, single-source guide through some of topology's most captivating facets. Contents PRELIMINARIES Product Topology Continuous Decompositions Homotopy and Fundamental Group Geometric Complexes and Polyhedra Complete Metric Spaces Compacta Continua Hyperspaces References INVERSE LIMITS AND RELATED TOPICS Inverse Limits Inverse Limits and the Cantor Set Inverse Limits and Other Operations Chainable Continua Circularly Chainable and P–like Continua Universal and A–H Essential Maps References JONES’S SET FUNCTION T The Set Function T Continuity of T Applications References A THEOREM OF E. G. EFFROS Topological Groups Group Actions and a Theorem of Effros References DECOMPOSITION THEOREMS Jones’s Theorem Detour to Covering Spaces Rogers’s Theorem Case and Minc–Rogers Continua Covering Spaces of Some Homogeneous Continua References n–FOLD HYPERSPACES General Properties Unicoherence Aposyndesis Arcwise Accessibility Points that Arcwise Disconnect C*n–smoothness Retractions Graphs Cones References QUESTIONS Inverse Limits The Set Function T Homogeneous Continua n–fold Hyperspaces References Index Sergio Macias is a professor at the Institute de Matematicas, Universidad Nacional Autonoma de Mexico, Mexico City.

Foundation Course in Statistical and Quantitative Reasoning - B.M.Aggarwal

Author

B.M. Aggarwal

Cover Price : Rs 375.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789385259722
YOP : 2015

Binding : Paperback
Total Pages : 296
CD : No

About the Book The book has been designed specifically for Foundation Course in Statistical and Quantitative Reasoning, for MBA. Keeping in view the fast that some of the students may be from Non mathematics back ground, the concepts have been explained elaborately to make the subject easily graspable by those students also, the syllabus has been covered fully. Keeping in view the time constraint of the students. The subject has been dealt to the point but omitting thing nothing which is otherwise required for the students. I hope, that the book will serve its purpose to the either satisfaction of the teachers and students. Contents • Matrices and Determinants • Preparation of Frequency Distribution • Statistical Averages (Measures of Central Tendency) • Measures of Variation • Measurement for Scale (Nominal Scale, Ordinal Scale, Interval Scale, Ratio Scale) • Basic Concept of Probability About the Author B.M.Aggarwal graduated with Honors in Mathematics from Punjab University followed by Masters degree in Mathematics from Meerut University and a degree in Electronics and Telecommunication Engineering from the Institute of Electronics and Telecommunications Engineering, Lodhi Road, New Delhi. A versatile teacher and a reputed Professor of Mathematics, Statistics and Operations Research the author has served in many reputed Management Institute in Delhi and NCR. His presentation can be seen through his lucid and logical treatment of the text.

Functional Analysis and Valuation Theory - Lawrence Narici

Author

Lawrence Narici
Edward Beckenstein
George Bachman

Cover Price : Rs 3,995.00

Imprint : CRC Press
ISBN : 9780824714840
YOP : 2015

Binding : Hardback
Total Pages : 200
CD : No

Functional Analysis and Valuation Theory presents some of the principal results of the theory of normed spaces and algebras over arbitrary fields with valuation. Most of the material included has not previously appeared in any other book. The reader need not have prior knowledge of valuation theory: necessary principles are discussed in the opening chapter. The book includes versions of the Banach-Steinhaus theorem, the Fredholm Alternative theorem, and the Hahn-Banach theorem. Normed algebras over valued field are also investigated at some length. Topics discussed include topolgizing the space of maximum ideals, a Stone-Weierstrass theorem, and a representation theorem analogous to that for complex B* -algebras. So that this work can be used as a text, exercises have been included wherever possible. Some are to be employed as practice exercises while others explore topics only mentioned in the main body of the book. A number of examples with various special properties are presented in the Appendix. In addition, an index of symbols and an extensive bibliography of pertinent literature in the field have also been provided. The book can be used a first or second year graduate text for students with a back ground in the classical theory of normed spaces and algebra, and will be of interest to mathematicians concerned with functional analysis and valuation theory. Contents PERFACE 1. TOPOLOGICAL RESULTS 1.1 Elementary Considerations 1.2 A Metrization Theorem 1.3 The Index of a Nonarchimedean Space 1.4 Local Compactness Exercises 1 2.COMPLETENESS 2.1 Spherical Completeness and Pseudo-Completeness 2.2 Countable Linear Compactness 2.3 Maximal Completeness and Pseudo-Completeness 2.4 The Existence of a Maximal Completion 2.5 F-Convexity and c-Compactness Exercises 2 3. NORMED LINEAR SPACES 3.1 The Residue class Space 3.2 Local Compactness 3.3 The Hahn-Banach Theorem 3.4 The Banach-Steinhaus Theorem 3.5 Completely Continuous Operators and the Fredholm Alternative Theorem 3.6 The Resolvent Set of a Linear Operator Exercises 3 4. NORMED ALGEBRAS 4.1 Normal Algebras: Mazur-Gelfand Theorem 4.2 The Spectrum 4.3 Maximal Ideals 4.4 The Gelfand Subalgebra 4.5 Topologizing the Maximal Ideals 4.6 Regular Algebras 4.7 Algebraic Algebras 4.8 V*-Algebras 4.9 Function Algebras 4.10 The Tietze Extension Theorem and Stone-Weierstrass Theorem 4.11 Representation Theorems Exercises 4 APPENDIX: EXAMPLES Index of Symbols Index LAWRENCE NARICIteaches mathematics at St. John's University, Jamaica, New York. His particular research interest is in functional analysis and valuation theory. Dr. Narici has written or collaborated on 17 books and res-arch papers. Dr. Narici received his Ph.D. at the Polytechnic Institute of Brooklyn. In the past, he served as consultant to IBM and to the Mount Sinai School of Medicine in conjunction with their biomedical engineering program. His memberships include the American Mathematical Society, the Mathematical Association of America, and the American Association of University Professors. EDWARD BECKEN STEINcurrently teaches mathematics at the Polytechnic Institute of Brooklyn, where he received his Ph.D. He has written 13 research papers, mostly in the areas of functional analysis and valuation theory. Dr. Beckenstein was consultant to GE and to the Mount Sinai School of Medicine in connection with their biomedical engineering program. Dr. Beckenstein belongs to the American Mathematical Society, the Mathematical Association of America, and the American Association of University Professors. GEORGE BACHMANteaches mathematics at the Polytechnic Institute of Brooklyn. Previously, he taught at Rutgers University. Many of the 23 research papers and books that he has written are on functional analysis and measure theory. Dr. Bachman received his Ph.D. in Mathematics at the Courant Institute of Mathematical Sciences, New York University. he is a member of the American Mathematical Society, the Mathematical Association of America, and the American Association of University Professors.

Probability and Numerical Methods, 4th Edn - J.P. Singh

Author

J.P. Singh

Cover Price : Rs 450.00

Imprint : Ane Books Pvt. Ltd.
ISBN : 9789388264471
YOP : 2018

Binding : Paperback
Size : 6.25
Total Pages : 436
CD : No

About the Book The fourth edition of Probability and Numerical Methods is the result of the enthusiastic reception given to the earlier editions received from the students and the teachers who are the end users of this book. The book covers the complete syllabus of BCA, semester IV of GGSIP University. It introduces Probability and Numerical Methods at undergraduate level in a simplified manner. Salient features • Text is self-explanatory and the language is vivid and lucid. • Contains numerous examples that illustrate the basic as well as high level concepts of the concerned topic. • Additional questions provided in all the chapters for practice. • Most of the questions conform to the trend in which the questions appear in GGSIP University. Contents 0. Elementary Concepts 1. Combinatorics: Permutation, Combination and Binomial Theorem 2. Probability-I 3. Probability-II 4. Random Variable and Mathematical Expectations 5. Discrete Probability Distributions 6. Normal Distribution 7. Finite Difference 8. Interpolation 9. Solution of Algebraic and Transcendental Equations 10. Solution of Linear Simultaneous Equations 11. Numerical Differentiation and Integration, Tables, End Term Examination About the Author J.P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has teaching experience of 19 years and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi. His areas of interest include Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation.

Algorithms for Linear Quadratic Optimization - Vasile Sima

Author

Vasile Sima

Cover Price : Rs 4,995.00

Imprint : CRC Press
ISBN : 9780824796129
YOP : 2015

Binding : Hardback
Total Pages : 380
CD : No

This up-to-date reference offers valuable theoretical, algorithmic and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems providing an overview of recent advances in control and systems theory, numerical line algebra, numerical optimization, scientific computations and software engineering. Examining state-of-the-art linear algebra algorithms and associated software, Algorithms for Linear-Quadratic Optimization presents algorithms in a concise, informal language that facilitates computer implementation…discusses the mathematical description, applicability, and limitations of particular solvers…summarizes numerical comparisons of various algorithms…highlights topics of current interest, including H∞ and H₂ optimization, defect corrections, and Schur and generalized Schur vector methods...emphasizes structure-preserving techniques… contains many worked examples based on industrial models… covers fundamental issues in control and systems theory such as regulator and estimator design, state estimation, and robust control…and more. Furnishing valuable references to key sources in the literature, Algorithms for Linear-Quadratic Optimization is an incomparable reference for applied and industrial mathematicians, control engineers, computer programmers, electrical and electronics engineers, systems analysts, operations research specialists, researchers in automatic control and dynamic optimization, and graduate students in these disciplines. Contents PREFACE LINEAR-QUADRATIC OPTIMIZATION PROBLEMS NEWTON ALGORITHMS SCHUR AND GENERALIZED SCHUR ALGORITHMS STRUCTURE-PRESERVING ALGORITHMS APPENDIXES COMPARISON OF RICCATI SOLVERS NOTATION AND ABBREVIATIONS INDEX OF ALGORITHMS DEFINITIONS INDEX About the Author Vasile Sima is Senior Research Fellow and Vice-President of the Scientific Council of the Research Institute for Informatics, Bucharest, Romania. The author or coauthor of several books and more than 80 professional publications, Dr. Sima serves on the editorial board of Studies in Informatics and Control. He is a member of the Numerical Analysis Network and an affiliate member of the International Federation of Automatic Control. Dr. Sima received the M.S.degree (1972) in control engineering from the Polytechnic University of Bucharest, Romania, the M.S.degree (1978) in mathematics from the University of Bucharest, Romania, and the Doctor of Engineering degree (1983) in electrical engineering from the Polytechnic University of Bucharest, Romania.

Complex Analysis - Pratiksha Saxena

Author

Pratiksha Saxena

Cover Price : £ 34.95

Imprint : Athena Academic
ISBN : 9781910390276
YOP : 2016

Binding : Hardback
Size : 6.25" X 9.50"
Total Pages : 296
CD : No

About the Book This book has been designed keeping in mind the needs of the readers for conceptual excellence and analytically evident examples that would help understand the subject better. The basic concepts are well supported with explanatory graphs, solved and unsolved examples. To develop mathematical skills and bring about clarity of theorems, a large number of carefully graded exercises are given with working rulesand the step by step methods of problem solving. We hope this book is very useful for students as well as for academicians. Salient Features Comprehensively explained theorem proofs Step by step solution of examples 220 solved examples Figures and graphs for better representation of concepts Contents 1. Pre-requisite. 2. Function, Limit and Continuity. 3. Complex Differentiation and Analytic Function. 4. Power Series. 5. Bilinear Transformation. 6. Conformal Mapping. 7. Complex Integration. 8. Zero and Singularities of A Function. 9. The Calculus of Residues. 10. Uniform Convergence of Sequence and Series. 11. Memomorphic Function. Concept definition and explanation in easy language About the Editor Dr. Pratiksha Saxena, currently teaching at the Department of Applied Mathematics, Gautam Buddha university, Greater Noida, India, has to her credit three books published with international publishers besides several papers in international journals. She has developed several books for Maharshi Dayanand university and Calicut university. A Gold Medalist in her post-graduation, she was awarded the prestigious Book Pal Memorial award at university Level. She has three Copyrights/Patents for simulation tools. She has been teaching both graduate and post-graduate students for the last sixteen years. She is the editorial board member and reviewer for a number of journals. Her research interests are in the areas of application of non-linear programming, optimization, modeling and simulation.


   

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