Fourier Series is a concise introduction to Fourier series covering history, major themes, theorems, examples, and applications. It can be used to learn this subject, and also to supplement, enhance, and embellish undergraduate courses on mathematical analysis. The book begins with a description of the problem that led Fourier to introduce his famous theory and a brief summary of the rich history of the subject over three centuries. The subject is presented in a way that enables the reader to appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity, and convergence. The abstract theory provides unforeseen applications in diverse areas. Examples, exercises, and directions for further reading and research are given, along with a chapter that provides material at a more advanced level suitable for graduate students. The author demonstrates applications of the theory as well as a broad range of problems. Exercises of varying levels of difficulty are scattered throughout the book. These will help readers test their understanding of the material.

"In the hands of a skillful instructor or a sufficiently imaginative reader, this book can be a gem and will provide the reader with significant insight into modern analysis."

Donald E. Meyers Source: Science Books and Films, AAAS

"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 Source: SIAM Reviews