Symmetry and Separation of Variables

by Willard Miller

Overview

Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.

Product Details

ISBN-13:	9780521177399
Publisher:	Cambridge University Press
Publication date:	03/29/2012
Series:	Encyclopedia of Mathematics and its Applications , #4
Edition description:	Reprint
Pages:	318
Product dimensions:	6.14(w) x 9.21(h) x 0.67(d)

Table of Contents

Editor's statement; Section editor's statement; Preface; 1. The Helmholtz equation; 2. The Schrödinger and heat equations; 3. The three-variable Helmholtz and Laplace equations; 4. The wave equation; 5. The hypergeometric function and its generalizations; Appendices; References; Index.

Editorial Reviews

Review of the hardback: ' … an important step in the group-theoretic approach to special functions. It is clearly written and should be accessible to a broad spectrum of readers'. Mathematical Reviews

From the Publisher