Title: Calculus of Variations - With Applications to Physics and Engineering (International Series in Pure and Applied Mathematics)
Publisher: Weinstock Press 2007-03-15
Publication Date: 2007
Language: English
ISBN 10: 1406756652
ISBN 13: 9781406756654
Binding: Paperback
Condition: New

About this title

Synopsis

This text is in two sections. the first part dealing with, background material, basic theorems and isoperimetric problems. The second part devoted to applications, geometrical optics, particle dynamics, he theory of elasticity, electrostatics, quantum mechanics and much more. Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Synopsis

Text extracted from opening pages of book: International Series in Pure and Applied Mathematics WILLIAM TED MARTIN, Consulting Editor Calculus of Variations International Series in Pure and Applied Mathematics WILLIAM TED MARTIN, Consulting Editor GOLOMB and SHANKS Elements of Ordinary Differential Equations LASS Vector and Tensor Analysis LEIGHTON An Introduction to the Theory of Differential Equations NEHARI Conformal Mapping SNEDDON Fourier Transforms WEINSTOCK Calculus of Variations CALCULUS OF VARIATIONS With Applications to Physics and Engineering Robert Weinstock Acting Assistant Professor in Mathematics tita nford I ' nivcrsity FIRST EDITION New York Toronto London McGRAW-HILL BOOK COMPANY INC. 1952 CALCULUS OF VARIATIONS Copyright, 1952, by the McGraw-Hill Book Company, Inc. Printed in the United States of America. All rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of the publishers. Library of Congress Catalog Card Number: 51-12654 THE MAPLE PRESS COMPANY, YORK, PA. To Betty PREFACE There seems to have been published, up to the present time, no English language volume in which an elementary introduction to the calculus of variations is followed by extensive application of the subject to problems of physics and theoretical engineering. The present volume is offered as partial fulfillment of the need for such a book. Thus its chief purpose is twofold : ( i) To provide for the senior or first-year graduate student in mathe matics, science, or engineering an introduction to the ideas and techniques of the calculus of variations. ( The material of the first seven chapters with selected topics from the later chapters has been used several times as the subject matter of a 10-week course in the Mathematics Department at Stanford University.) ( ii) To illustrate the application of the calculus of variations in several fields outside the realm of pure mathematics. ( By far the greater emphasis is placed upon this second aspect of the book's purpose.) The range of topics considered may be determined at a glance in the table of contents. Mention here of some of the more significant omis sions may be pertinent: The vague, mechanical d method is avoided throughout. Thus, while no advantage is taken of a sometimes convenient shorthand tactic, there is eliminated a source of confusion which often grips the careful student when confronted with its use. No attempt is made to treat problems of sufficiency or existence: no consideration is taken of the second variation or of the conditions of Legendrc, Jacobi, and Weicrstrass. Besides being outside the scope of the chief aim of this book, these matters are excellently treated in the volumes of Bolza and Bliss listed in the Bibliography. Expansion theorems for the eigenfunctions associated with certain boundary-value problems are stated without proof. The proofs, beyond the scope of this volume, can be constructed, in most instances, on the basis of the theory of integral equations. Space limitations prevent inclusion of such topics as perturbation theory, heat flow, hydrodynamics, torsion and buckling of bars, Schwingcr's treatment of atomic scattering, and others. However, the reader who has mastered the essence of the material included should have little difficulty in applying the calculus of variations to most of the subjects which have been squeezed out. viii PREFACE It is hardly necessary to mention the debt I owe to nearly all the works mentioned in the Bibliography; Courant-Hilbert has been especially helpful. In the early stages of the work, comments from my former students Gordon Kent and Peter Szego were useful. Occasional chats with colleagues in the Stanford Mathematics Department were simi larly helpful. I owe a tremendous debt of gratitude to my wife, Elizabeth B. Weinstock, whose keen critical faculty is responsible for several important corrective changes in the text, who worked out nearly all the exercises, who did all

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