Fourier Analysis and Its Applications (Graduate Texts in Mathematics, Vol. 223)

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Product Description

A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.

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Fourier Analysis and Its Applications (Graduate Texts in Mathematics, Vol. 223) Review

I have waited for some professional mathematician to review this book, since I think it is such a good book. This has not happened, so here is my un-professional review:

I am a retired electrical engineer, and the last three years I have worked on refreshing my old and forgotten school math, and also to going a bit further than during school. When I bought this book I had the following wishes, all of whom it fulfilled brilliantly:

1. It should be usable for self study.

2. It should refresh my fourier series and transforms.

3. It should put these things in context, by presenting physics problems and also by widening the scope to wet the appetite for functional analysis and partial diff eqs.

4. It should do something for my sorely lacking "mathematical maturity".

All of these things it did and I just want to add that Mr. Vretblad is an outstanding pedagogue and that the book contains very few typos. (I found two or three in the whole book, none of them important).

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