Fomin himself, and 2) A variety of helpful suggestions from Professor J. In so doing, I have had two special assets : 1) A substantial list of revisions and corrections from Professor S. With the authors' consent, I have given free rein to the tendency of any mathe matically educated translator to assume the functions of annotator and stylist. The present edition is rather different from the Russian original. This book is a modern int1 oduction to the calculus of variations and certain of its ramifications, and I trust that its fresh and lively point of view will serve to make it a welcome a tldition to the English-language literature on the subject. Kostyuchenko, who read the book in manuscript and made many useful comments. Chapter 8 contains a brief treat ment of direct methods in the calculus of variations. Chapter 7 is devoted to the application of variational methods to the study of systems with infinitely many degrees of freedom. The first six chapters contain, more or l ess, the material given in the usual university course in the calculus of variations (with applications to the m echanics of systems with a finite number of degrees of freedom ), including the theory of fields (presented in a somewhat novel way ) and sufficient conditions for w eak and strong extrema. The first three chapters, taken together, form a more compre hensive course on the elements of the calculus of varia tions,-but one which is still quite elementary (involving only n ecessary conditions for extrema). The reader who merel y wishes to b ecom e familiar with the most basic concepts and methods of the calculus of variations need only study the first chapter. ![]() , canonical equations, variational principles of mechanics and conservation laws. ![]() Considerable attention is d evoted to physical applica tions of variational methods, e. Our aim is to give a treatment of the ele ments of the calculus of variations in a form which is both easily understandable and sufficiently modem. However, the book goes considerably b eyond the material actually pres ented in the lectures. Gelfand in the Mechanics and Mathematics D epartment of Moscow State University. The pres ent course is bas ed on l ectures given by I. Library of Congress Catalog Card Number 63-18806 Printed in the United States of America PRENTICE-HALL OF CANADA, LID., TORONTO PRENTICE-HALL OF INDIA PRENTICE-HALL INTERNATIONAL, INC., LONDON PRENTICE-HALL OF AUSTRALIA, Mimeograph or any other means, without permission in writing from the publisher.Ĭurrent printing (last digit ) : 20 19 18 17 16 15 ![]() SELECTED RUSSIAN PUBLICATIONS IN THE MATHEMATICAL SCIENCES Richard A. FOMIN Moscow State University Revised English Edition Translated and Edited by
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