THEORY_AND_PROBLEMS_OF_BEGI.PDF

SCHAUM'S OUTLINE SERIES

Schaum's Outline of Theory and Problems of Beginning

Calculus

Second Edition

Elliott Mendelson, Ph.D.

Professor of Mathematics

Queens College

City University of New York

To the memory of my father, Joseph, and my mother, Helen

ELLIOTT MENDELSON is Professor of Mathematics at Queens College of the City University of

New York. He also has taught at the University of Chicago, Columbia University, and the University of

Pennsylvania, and was a member of the Society of Fellows of Harvard University. He is the author of

several books, including Schaum's Outline of Boolean Algebra and Switching Circuits. His principal

area of research is mathematical logic and set theory.

Schaum's Outline of Theory and Problems of

BEGINNING CALCULUS

States of America. Except as permitted under the Copyright Act of 1976, no part of this publication

may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval

system, without the prior written permission of the publisher.

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 PRS PRS 9 0 1 0 9

ISBN 0-07-041733-4

Sponsoring Editor: Arthur Biderman

Production Supervisor: Suzanne Rapcavage

Editing Supervisor: Maureen B. Walker

Library of Congress Cataloging-in-Publication Data

Mendelson, Elliott.

Schaum's outline of theory and problems of beginning calculus /

Elliott Mendelson, -- 2nd ed.

p. cm. -- (Schaum's outline series)

Includes index.

ISBN 0-07-041733-4 (pbk.)

1. Calculus. 2. Calculus--Problems, exercises, etc. I. Title.

QA303.M387 1997

515' .076--dc21 96-39852

CIP

Preface

This Outline is limited to the essentials of calculus. It carefully develops, giving all steps, the principles

of differentiation and integration on which the whole of calculus is built. The book is suitable for

reviewing the subject, or as a self-contained text for an elementary calculus course.

The author has found that many of the difficulties students encounter in calculus are due to weakness in

algebra and arithmetical computation, emphasis has been placed on reviewing algebraic and

arithmetical techniques whenever they are used. Every effort has been made—especially in regard to

the composition of the solved problems—to ease the beginner's entry into calculus. There are also some

1500 supplementary problems (with a complete set of answers at the end of the book).

High school courses in calculus can readily use this Outline. Many of the problems are adopted from

questions that have appeared in the Advanced Placement Examination in Calculus, so that students will

automatically receive preparation for that test.

The Second Edition has been improved by the following changes:

1. A large number of problems have been added to take advantage of the availability of graphing

calculators. Such problems are preceded by the notation . Solution of these problems is not

necessary for comprehension of the text, so that students not having a graphing calculator will not

suffer seriously from that lack (except insofar as the use of a graphing calculator enhances their

understanding of the subject).

2. Treatment of several topics have been expanded:

( a ) Newton's Method is now the subject of a separate section. The availability of calculators makes

it much easier to work out concrete problems by this method.

( b ) More attention and more problems are devoted to approximation techniques for integration, such

as the trapezoidal rule, Simpson's rule, and the midpoint rule.

( c ) The chain rule now has a complete proof outlined in an exercise.

3. The exposition has been streamlined in many places and a substantial number of new problems have

been added.

The author wishes to thank again the editor of the First Edition, David Beckwith, as well as the editor of

the Second Edition, Arthur Biderman, and the editing supervisor, Maureen Walker.

ELLIOTT MENDELSON

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