tailieunhanh - Ebook Advanced calculus: Part 1

(BQ) Part 1 book "Advanced calculus" has contents: Introduction, Vector spaces, finite dimensional vector spaces, the differential calculus, the differential calculus, scalar product spaces, scalar product spaces. | L Y N N H. L 0 0 MIS and S H L 0 M 0 S T ERN B ERG Department of Mathematics, Harvard University ADVANCED CALCULUS REVISED EDITION JONES AND BARTLETT PUBLISHERS Boston London , ~"\' ~ ", :,i.; J) Editorial, Sales, and Customer Service Offices: Jones and Bartlett Publishers, Inc, One Exeter Plaza Boston, MA 02116 Jones and Bartlett Publishers International POBox 1498 London W6 7RS England Copyright © 1990 by Jones and Bartlett Publishers, Inc. Copyright © 1968 by Addison-Wesley Publishing Company, Inc. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from the copyright owner. Printed in the United States of America. 10 9 8 7 6 5 4 3 2 Library of Congress Cataloging-in-Publication Data Loomis, Lynn H. Advanced calculus / Lynn H. Loomis and Shlomo Sternberg. -Rev. ed. p. cm. Originally published: Reading, Mass. : Addison-Wesley Pub. Co., 1968. ISBN 0-86720-122-3 1. Calculus. I. Sternberg, Shlomo. II. Title. 1990 89-15620 515--dc20 CIP 'I '. , PREFACE This book is based on an honors course in advanced calculus that we gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in anyone year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. These prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of .