Fourier Series and Boundary Value Problems

Ruel Vance Churchill

ISBN 10: 0070108439 / ISBN 13: 9780070108431

Published by McGraw-Hill Companies, 1978

Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 1.1. Seller Inventory # G0070108439I3N00

Synopsis:

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.

Bibliographic Details

Title: Fourier Series and Boundary Value Problems
Publisher: McGraw-Hill Companies
Publication Date: 1978
Binding: Paperback
Condition: Good
Dust Jacket Condition: No Jacket
Edition: 3rd Edition