Brown J.W., Churchill R.V. Fourier Series and Boundary Value Problems

8th Edition. — McGraw-Hill, 2012. — 418 p. — (Brown and Churchill Series). — ISBN 978-0-07-803597-5.Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus.
There are two main objectives of this text. The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations.
The book is a thorough revision of the seventh edition and much care is taken to give the student fewer distractions when determining solutions of eigenvalue problems, and other topics have been presented in their own sections like Gibbs' Phenomenon and the Poisson integral formula.Partial Differential Equations of Physics
The Fourier Method
Boundary Value Problems
Fourier Integrals and Applications
Orthonormal Sets
Sturm-Liouville Problems and Applications
Bessel Functions and Applications
Legendre Polynomials and Applications
Verification of Solutions and Uniqueness
AppendixesSome Fourier Series Expansions
Solutions of Some Regular Sturm-Liouville Problems
Some Fourier-Bessel Series Expansions