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Fourier Series, by Georgi P. Tolstov
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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.
- Sales Rank: #2682193 in Books
- Published on: 2014-10-11
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .78" w x 6.14" l, 1.18 pounds
- Binding: Paperback
- 350 pages
Most helpful customer reviews
82 of 84 people found the following review helpful.
excellent introduction
By Garrett H. Hansen
This book is a great introduction to the theory of Fourier series. If, like me, you're starting from scratch with a healthy calc background, you'll have no trouble using this book for self-study. The exercises are not trivial, but they won't take an hour each (like Whittaker & Watson).
My one gripe is that, aside from trig systems, Fourier-Bessel systems, and one paragraph on Legendre polynomials, they fail to give any other examples of complete orthogonal systems. If you're looking for a general book on orthogonal functions, this is not it. It is, however, a perfect introduction to the Fourier theory.
41 of 41 people found the following review helpful.
Great Book
By L. Bovard
This is an excellent book on Fourier series! All you need is first year calculus to understand most of what is going on in this book. However it is quite mathematical in nature and if you are looking for just a quick introduction without much fuss, than look elsewhere. If you are, like me, interested in more of the theory of Fourier Series then this book is excellent.
As another reviewer pointed out the book only covers trig Fourier and Fourier-Bessel series which is unfortunate. I am using this book in aide of learning PDEs and I have to say all the books on PDEs I've read do not have an adequate discussion of Fourier-Bessel series other than their possible existence and the other relationships you can derive from Sturm-Liouville theory.
The problems in Chapter 9 are excellent applications of Fourier Series in the study of PDEs. I should note that another HUGE plus to this book is that the answer to every question is in the back making it ideal for self-study.
36 of 38 people found the following review helpful.
Very very good one
By Rakesh
Can't say anything wrong about this book. Initially I bought this because I wanted to get a little more out of the PDE. But man, after the reading the first 2 chapters, I was hooked on the subject. The most interesting matter happens in 3, 4 and 5 and after that it gets really really good when he talks about Bessel functions and Eigenfunction methods in the last 2 chapters.
I would say this is an excellent book on the subject matter. This is one of those extremely rare books that when you complete a page and flip, you will never have to flip back to recall. The explanation sticks to your mind perfectly.
I think that I have understood many other topics well once I learned a little bit about fourier analysis. Some of the ideas such as convergence of fourier-bessel functions and almost every topic in chapter 9 is very well presented and useful in many other classes where particular books skip (or save pages) on these vital topics.
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