This text not only provides a simple and easy-to- read-the-first-time guide to solving PDEs with Fourier series, it also is chock-full with all the necessary details and includes many interesting problems. I took a course out of this book as a sophomore in college and found it very interesting and useful. The style and difficulty is very similar to a typical undergraduate ordinary differential equations book, except this is better organized.The subjects include a small bit on characteristics for first-order equations, a chapter on trigonometric series, PDEs in rectangular, polar, and spherical systems and associated eigenfunction expansions, Sturm-Liouville theory, the fourier transform, Laplace/Hankel transforms for PDEs, grid-type numerical methods, sampling & discrete Fourier analysis, and quantum mechanics (the Schroedinger equation).
This book is definitely great for applied mathematicians, physicists, or engineers who really need a solid introduction to the topic, written by someone who knows all the details. Any treatment in "mathematical physics" courses on PDEs will fall short of this book's content.
Of particular importance are the inclusion of special sections for Bessel functions, Legendre polynomials, associated Legendre functions, spherical harmonics, etc. All the details of solution and many exercises are included.
The most interesting parts of the book are towards the end, with the Sampling Theorem and discrete Fourier transform; and the proof of Heisenberg's uncertainty principle.
This book is also useful for more theoretical mathematicians or mathematical physicists who need an introduction to PDEs before taking a more difficult course on general theory.
In short, I think that even though this book is of great utility to non-mathematicians, it is proper to learn these concepts and techniques in a proper math setting where care is taken. This text is a solid foundation for confident application and a springboard towards more advanced subjects.
