Fourier Series

by Georgi P. Tolstov, Richard A. Silverman (Translator)

2014 Reprint of 1962 Edition. Full facsimile of the original edition. Not reproduced with Optical Recognition Software. The present volume is an introduction to Fourier series and their use in solving boundary value problems of mathematical physics. The text treats expansions in Fourier series, general orthogonal expansions, convergence of Fourier series, operations with Fourier series, double Fourier series, Fourier integrals and transforms, Bessel functions and Fourier-Bessel series, the eigenfunction method and its use in solving boundary value problems of mathematical analysis, applications to vibrating systems and heat flow problems. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text. Tolstov was one of the foremost mathematicians of the former Soviet Union.

Genres: Mathematics, Reference, Physics, Science, Textbooks, Engineering, Nonfiction

348 pages, Paperback

First published June 1, 1976

Reviews

[Cjn · Rating 4 out of 5]

These Dover mathematics books can be really hit or miss. I found this one clear and relatively accessible for someone without such a solid math background (natural scientist with some college calculus).

[Roi Orzach · Rating 5 out of 5]

The Fourier Series is a family of a series of infinite trigonometric functions. This book does an excellent job at explaining the mathematics behind this important topic. With most math books, there is a large amount of assumed knowledge, leaving the book largely unreadable to the “common joe.” While this is in no way a book for the ordinary person, anyone with a sound knowledge of calculus and a rough understanding of real analysis will be able to comprehend and enjoy this book. With every new topic there are a plethora of insightful examples to help reinforce the topic. My major complaint is that the proofs are rather free hand. The author whimsically interchanges derivatives, summations, and integrals without explaining why this is correct. In addition, a lot of the proofs leave out a large amount of steps, or merely deem the result as trivial. This is one of the books my professor calls a “read with notepad ready book.” This is because to fully understand the material, one must also work out the solutions on their own. Near the end of the book is where the applications appear. Fourier series are used to describe wave natures and heat transfer. The examples are insightful and show how truly important this mathematical concept is. The intentions of this book are to explain the theory and applications of the Fourier Series. If the following phrases “absolutely integrable over a closed and bounded interval,” “necessary and sufficient condition for pointwise continuity,” and “jump discontinuities” made anyone’s inner math nerd crave more information, then to those people I would recommend this book.

[Haochen Zhang · Rating 5 out of 5]

Finished the book hoping to read something about Fourier transforms. It turned out to be a really nice book on Fourier series.

[Talha]

Itiraf ediyom (A Confession): "Yazarinin soyadi Tolstoy'unki gibi ya. :|" diye aldim bu kitabi. Tercih yaparken muhakeme zayif duserse boyle antin kuntin kistaslara meylediyo iste insan.

[Jovany Agathe · Rating 4 out of 5]

Awesome

[Tawfeeq Amro · Rating 5 out of 5]

Best Book explain Fourier Series! this man are amazing .