文档介绍：Jerrold Marsden
University ofCalifornia, Berkeley
Alan Weinstein
University ofCalifornia, Berkeley
The Benjamin/Cummings pany, Inc.
Menlo Park. California - Reading, Massachusetts
London - Amsterdam - Don Mills. Ontario - Sydney
Sponsoring Editor: Susan A. Newman
Production Editor: Madeleine S. Dreyfack
To Alison, Christopher, Asha, and the future ofcalculus.
Copyright © 1981 by The Benjamin/Cummings pany, Inc.
Philippines copyright © 1981 by The Benjamin/Cummings pany,
Inc.
All rights reserved. No part of this pUblication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means,
electronic, mechanical, photocopying, recording, or otherwise, without
the prior written permission of the publisher. Printed in the United
States of America. Published simultaneously in Canada.
Library of Congress Cataloging in Publication Data
Marsden, Jerrold E.
Calculus unlimited.
Includes index.
1. Calculus. I. Weinstein, Alan, 1943- joint
author. II. Title.
515 80-24446
ISBN 0-8053-6932·5
ABCDEFGHIJ-AL-83 21 0
The Benjamin/Cummings pany, Inc
2727 Sand Hill Road
Menlo Park, California 94025
.Preface
Purpose
This book is intended to supplement our text, Calculus (Benjamin!
Cummings, 1980), or virtually any other calculus text (see page vii, How To
Use This Book With Your Calculus Text). As the title Calculus Unlimited
implies, this text presents an alternative treatment ofcalculus using the method
of exhaustion for the derivative and futegral in place of limits. With the aid of
this method, a definition of the derivative may be introduced in the first lecture
of a calculus course for students who are familiar with functions and graphs.
Approach
Assuming an intuitive understanding of real numbers, we begin in Chapter
1 with the defmition of the derivative. The axioms for real numbers are pre•
sented only when needed, in the discussion of continuity. Apart from this,