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084f2db8c6 The second edition, like the first, is divided into two volumes. Bohnenblust, A. In grateful acknowledgment 1 happily dedicate this book to her. The concept of the integral is defined first for step functions. ISBN 0 471 00005 1 Library of Congress Catalog Card Number: 67-14605 Printed in the United States of America. 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. Proofs of a11 the important theorems are presented as an essential part of the growth of mathematical ideas; the proofs are often preceded by a geometric or intuitive discussion to give the student some insight into why they take a particular form. It provides a natural blending of algebra and analysis and helps pave the way for the transition from one- variable calculus to multivariable calculus, discussed in Volume II. As the student learns the properties of the integral for step functions, he gains experience in the use of the summation notation and at the same time becomes familiar with the notation for integrals.
A. The staff of the Blaisdell Publishing Company has, as always, been helpful; 1 appreciate their sym- pathetic consideration of my wishes concerning format and typography. INTRODUCTION Part 1. 1 0 9 8 7 6 5 4 3 2 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. Finally, it gives me special pleasure to express my gratitude to my wife for the many ways she has contributed during the preparation of both editions. A glance at the table of contents reveals that the book has been divided into smaller chapters, each centering on an important concept. Pasadena, California September 16, 1966 CONTENTS 11.1 1 1.2 1 1.3 *1 1.4 1 1.5 1 1.6 12.1 1 2.2 12.3 1 2.4 1 2.5 13.1 1 3.2 *1 3.3 1 3.4 *1 3.5 1 3.6 1. While treating the calculus as a deductive science, the book does not neglect applications to physical problems. 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. vii .