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.
The present edition of the book is a revised version of the original one with many changes and additions, including some subsections, making it better readable and also giving better motivations and clarifications for many of the results.
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.
Contents
1. Sequence and Series of Real Numbers 2. Limit, Continuity and Differentiability of Functions
3. Definite Integral 4. Improper Integrals 5. Sequence and Series of Functions 6. Fourier Series
References, Index
About the Author
Dr. M. Thamban Nair is a Professor of Mathematics at IIT Madras. He did his Ph.D. at IIT Bombay and was a Post Doctoral Fellow at University of Grenoble (France). He held visiting positions at Australian National University, Canberra, (Australia), University of Kasiserslautern (Germany), Sun Yat-sen University, Guangzhou (China), University of Saint Etienne (France) and Weierstrass Institute for Applied Analysis and Stochastics, Berlin (Germany). He published more than 75 research papers in national and international journals in the areas of spectral approximations, operator equations, and inverse and ill-posed equations. He is author of the books “Functional Analysis: A First Course”, “Linear Operator Equations: Approximation and Regularization”, “Measure and Integration: A First Course”, and co-author of “Linear Algebra”. He has won many awards including the “C.L. Chandana Award for Distinguished and Outstanding Contributions to Mathematics Research and Teaching in India for the year 2003”. |