Variational Methods for Eigenvalue Problems: An Introduction to the Methods of Rayleigh, Ritz, Weinstein, and Aronszajn

Gould, S. H.

ISBN 10: 0486687120 / ISBN 13: 9780486687124

Published by Dover Publications, 1995

About this Item

Softcover book in FINE condition. Actual book is pictured. See images provided. Minimal shelfwear. All pages clean without any notations, underlinings or folds. Synopsis The importance of eigenvalue theory in pure and applied mathematics, and in physics and chemistry, makes it incumbent on students to understand the various methods of approximate calculation of eigenvalues. It is especially important to develop such methods in a general and theoretical manner, if only to avoid missing opportunities for particular applications. This book does just that, approaching the topic from a purely mathematical standpoint. Because variational methods are particularly well adapted to successive approximation, this book gives a simple exposition of such methods, not only of the familiar Rayleigh-Ritz method, but especially of the related methods the Weinstein method, Weinstein-Aronszajn method, and others. To make the book accessible to a broad range of students, little mathematical knowledge is presupposed beyond the elements of calculus. Where specialized knowledge is required as it is in the discussion of direct methods in the calculus of variations and the theory of completely continuous operators in Hilbert space the requisite material is developed in full. The first nine chapters, written in elementary style, discuss the general theory of variational methods with special reference to the vibrating plate. In the last chapter, the information gained thereby is extended, in a less elementary way, to more general cases. Exercises are provided throughout to illuminate the ideas and methods developed in the text. "About this title" may belong to another edition of this title.

Seller Inventory # 241021

Bibliographic Details

• Title: Variational Methods for Eigenvalue Problems: An Introduction to the Methods of Rayleigh, Ritz, Weinstein, and Aronszajn
• Publisher: Dover Publications
• Publication Date: 1995
• Language: English
• ISBN 10: 0486687120
• ISBN 13: 9780486687124
• Binding: Soft cover
• Condition: Fine

About this title

Synopsis

The importance of eigenvalue theory in pure and applied mathematics, and in physics and chemistry, makes it incumbent on students to understand the various methods of approximate calculation of eigenvalues. It is especially important to develop such methods in a general and theoretical manner, if only to avoid missing opportunities for particular applications. This book does just that, approaching the topic from a purely mathematical standpoint.
Because variational methods are particularly well adapted to successive approximation, this book gives a simple exposition of such methods, not only of the familiar Rayleigh-Ritz method, but especially of the related methods — the Weinstein method, Weinstein-Aronszajn method, and others.
To make the book accessible to a broad range of students, little mathematical knowledge is presupposed beyond the elements of calculus. Where specialized knowledge is required — as it is in the discussion of direct methods in the calculus of variations and the theory of completely continuous operators in Hilbert space — the requisite material is developed in full.
The first nine chapters, written in elementary style, discuss the general theory of variational methods with special reference to the vibrating plate. In the last chapter, the information gained thereby is extended, in a less elementary way, to more general cases. Exercises are provided throughout to illuminate the ideas and methods developed in the text.