文档介绍：Tom M. Apostol
CALCULUS
VOLUME 1
One-Variable Calculus, with an
Introduction to Linear Algebra
SECOND EDITION
John Wiley & Sons, Inc.
New York l Santa Barbara l London l Sydney l Toronto
CONSULTING EDITOR
e Springer, Indiana University
XEROX @ is a trademark of Xerox Corporation.
Second Edition Copyright 01967 by John WiJey & Sons, Inc.
First Edition copyright 0 1961 by Xerox Corporation.
Al1 rights reserved. Permission in writing must be obtained
from the publisher before any part of this publication may
be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopy, recording,
or any information storage or retrieval system.
ISBN 0 471 00005 1
Library of Congress Catalog Card Number: 67-14605
Printed in the United States of America.
1098765432
TO
Jane and Stephen
PREFACE
Excerpts from the Preface to the First Edition
There seems to be no general agreement as to what should constitute a first course in
calculus and analytic geometry. Some people insist that the only way to really understand
calculus is to start off with a thorough treatment of the real-number system and develop
the subject step by step in a logical and rigorous fashion. Others argue that calculus is
primarily a tool for engineers and physicists; they believe the course should stress applica-
tions of the calculus by appeal to intuition and by extensive drill on problems which develop
manipulative skills. There is much that is sound in both these points of view. Calculus is
a deductive science and a branch of pure mathematics. At the same time, it is very impor-
tant to remember that calculus has strong roots in physical problems and that it derives
much of its power and beauty from the variety of its applications. It is possible bine
a strong theoretical development with sound training in technique; this book represents
an attempt to strike a sensible balance between the two. While treating the calculus