Gerald B. Folland
Brad G. Osgood (Chair)
Cover art by Karen Mesterton-Gibbons.
2000 Mathematics Subject Classiﬁcation. Primary 49–01, 49K15, 49N05
49N35; Secondary 92–02, 92D50.
For additional information and updates on this book, visit
Library of Congress Cataloging-in-Publication Data
A primer on the calculus of variations and optimal control theory / Mik
p. cm. — (Student mathematical library ; v. 50)
Includes bibliographical references and index.
ISBN 978-0-8218-4772-5 (alk. paper)
1. Calculus of variations. 2. Control theory. 3. Mathematical optimizatio
Copying and reprinting. Individual readers of this publication, and nonproﬁ
libraries acting for them, are permitted to make fair use of the material, such as t
copy a chapter for use in teaching or research. Permission is granted to quote bri
passages from this publication in reviews, provided the customary acknowledgment
the source is given.
Republication, systematic copying, or multiple reproduction of any material in th
publication is permitted only under license from the American Mathematical Societ
Requests for such permission should be addressed to the Acquisitions Departmen
American Mathematical Society, 201 Charles Street, Providence, Rhode Island 0290
2294 USA. Requests can also be made by e-mail to email@example.com.
c 2009 by the American Mathematical Society. All rights reserved.
Reprinted with corrections by the American Mathematical Society, 2014.
The American Mathematical Society retains all rights
except those granted to the United States Government.
Printed in the United States of America.
∞ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability.
Visit the AMS home page at http://www.ams.org/
10 9 8 7 6 5 4 3 2 19 18 17 16 15 14