John Wiley & Sons - Calculus, Volume 1, One-Variable Calculus With An Introduction To Linear Algebra -.pdf
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
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