This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.
M. Thamban Nair is a Professor of Mathematics at the Indian Institute of Technology Madras, India. Prof. Nair has been a research mathematician and teacher for over 30 years for postgraduate- and undergraduate-level mathematics courses. He won many awards including the C. L. Chandana Award for distinguished and outstanding contributions in mathematics research and teaching in India for the year 2003. He was also a Post Doctoral Fellow at the University of Grenoble (France) and Visiting Professor at Australian National University, Australia, University of Kaiserslautern, Germany, Sun Yat-sen University, Guangzhou, China, and University of Saint Etienne, France. He gave several invited talks at various conferences in India and abroad. Professor Nair has got over 80 journal publications and 5 books to his credit. The broad area of Prof. Nair’s research is in applicable functional analysis, more specifically, spectral approximation, operator equations, and inverse and ill-posed problems.
