Mathematical Analysis - General & Miscellaneous, Mathematical Series, Vectors & Tensors, Mathematical Equations - Differential

Fourier Series and Boundary Value Problems

Name: Fourier Series and Boundary Value Problems
Author: James Ward Brown
ISBN: 9780073051932

by James Ward Brown, Ruel V. Churchill

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Overview

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.

Synopsis

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.