eBook - ePub
Variational Methods for Eigenvalue Problems
An Introduction to the Methods of Rayleigh, Ritz, Weinstein, and Aronszajn
- 192 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Variational Methods for Eigenvalue Problems
An Introduction to the Methods of Rayleigh, Ritz, Weinstein, and Aronszajn
About this book
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.
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.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Variational Methods for Eigenvalue Problems by S. H. Gould in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Quantum Theory. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- DOVER BOOKS ON MATHEMATICS
- Title Page
- Dedication
- Copyright Page
- PREFACE
- Table of Contents
- INTRODUCTION
- I - SYSTEMS VIBRATING WITH A FINITE NUMBER OF DEGREES OF FREEDOM
- II - VARIATIONAL PRINCIPLES FOR FINITE-DIMENSIONAL SYSTEMS
- III - VIBRATION OF SYSTEMS WITH INFINITELY MANY DEGREES OF FREEDOM
- IV - REPRODUCING KERNELS AND FUNCTIONAL COMPLETION
- V - VIBRATING RODS, MEMBRANES, AND PLATES
- VI - THE WEINSTEIN METHOD IN ITS ORIGINAL FORM
- VII - LINEAR OPERATORS IN HILBERT SPACE
- VIII - THE WEINSTEIN-ARONSZAJN METHOD FOR LINEAR OPERATORS IN HILBERT SPACE
- IX - APPLICATION OF THE WEINSTEIN-ARONSZAJN METHOD IN HILBERT SPACE TO THE DIFFERENTIAL PROBLEM OF THE VIBRATING PLATE
- X - APPLICATION OF THE APPROXIMATIVE METHODS TO GENERAL DIFFERENTIAL PROBLEMS
- BIBLIOGRAPHY
- INDEX