Fourier Series and Boundary Value Problems

by James Ward Brown, Ruel Vance Churchill

This is an introductory treatment of Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It is designed for students who have completed a first course in ordinary differential equations and the equivalent of a term of advanced calculus. In order that the book be accessible to as many students as possible, there are footnotes referring to texts which give proofs of the more delicate results in advanced calculus that are occasionally needed. The physical applications, explained in some detail, are kept on a fairly elementary level. The first objective of the book is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. Representations of functions by Fourier series involving sine and cosine functions are given special attention. Fourier integral representations and expansions in series of Bessel functions and Legendre polynomials are also treated. The second objective is a clear presentation of the classical method of separations of variables used in solving boundary value problems with the aid of those representations. Some attention is given to the verification of solutions and to uniqueness of solutions, for the method cannot be presented properly without such considerations. Other methods are treated in the authors' book Complex Variables and Applications, and in Professor Churchill's book, Operational Mathematics.

Genres: Mathematics, Textbooks, Nonfiction, Science, Reference

271 pages, Paperback

First published December 1, 1963

Reviews

[Dale Baker]

best book ever??? maybe...do you do applied math for a livin' like me part of the time...this is a classic text that can help you...no matter what your level of mathematical sophistication...I love it and have taught from it...I had an amazing teacher(s) that taught from it...Thank you Dr. Nemat Nassar and the late great Si Rand...who taught me so much applied math and physics in grad school..scholar and all round great mench...RIP ...i miss talking to you quietly...ok back to the book...if you need a primer on pde's this it...you can prove orthoganality and the uniqueness of solution...thank you dr. ghassan kassab for helping me with this (one of dr fung's academic sons....one of many that I am grateful too...

[Mi Lia · Rating 5 out of 5]

Really good introductory book in the theory of partial differential equations and the most important methods of solving them (pretty much: seperation of variables). Ideal for self-study.