Texts and Readings in Mathematics

Fourier Series (2/E)
Rajendra Bhatia

This book provides a quick introduction to Fourier Series. The author begins by describing one of the problems actually studied by Fourier and how this leads to a differential equation – to solve which Fourier introduced his famous series. The mathematical problems this leads to are then discussed rigorously. After that, applications of the theory to four different problems are given.

A novel feature of the book is the inclusion of a detailed history of the subject. This would help the student understand why this topic is important.

In the revised edition, Chapter 3 has been considerably expanded to include more examples and connections with related topics.

A large part of the book can be read by third year B.Sc. Hons students in India and can be used by them to supplement their analysis courses and to sharpen their understanding of concepts like convergence, uniform convergence etc. For some later portions a knowledge of Functional Analysis is required. These parts can be read by M.Sc. and M. Phil students. The book would also be useful for summer schools and refresher courses for students and college teachers. To such an audience all the material can be taught in about one month.
Reviews
"Bhatia's Fourier Series was a pleasure to read. Written clearly with a conversational tone, Fourier Series should appeal to a wide audience. Advanced undergraduates, just beginning their mathematical journey, will be encouraged by this text. Not only will they encounter many fundamental properties and interesting applications of Fourier series, they will also be exposed to some of the right history surrounding the subject. … The care and detail with which Bhatia writes coupled with a very personable presentation style, makes this book a welcome addition to my collection. … I will certainly use this book as a supplemental text in my PDE courses."
-- Roger Thelwell, SIAM Review
Contents
1. Heat Conduction and Fourier Series
2. Convergence of Fourier Series
3. Odds and Ends
4. Convergence in L2 and L1
5. Some Applications
Appendix

For sale in India only
Texts and Readings in Mathematics/ 2
Corrected Reprint 2010, 9788185931340, 184 pages, paper cover, Rs. 250.00