A First Course in Complex Analysis with Applications - Zill.pdf

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A First Course in
Complex
Analysis
with Applications
Dennis G. Zill
Loyola Marymount University
Patrick D. Shanahan
Loyola Marymount University
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Copyright © 2003 by Jones and Bartlett Publishers, Inc.
Library of Congress Cataloging-in-Publication Data
Zill, Dennis G., 1940-
A first course in complex analysis with applications / Dennis G. Zill, Patrick D. Shanahan.
p. cm.
Includes indexes.
ISBN 0-7637-1437-2
1. Functions of complex variables. I. Shanahan, Patrick, 1931- II. Title.
QA331.7 .Z55 2003
515’.9—dc21
2002034160
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in
any form, electronic or mechanical, including photocopying, recording, or any information storage or retrieval
system, without written permission from the copyright owner.
Chief Executive Officer: Clayton Jones
Chief Operating Officer: Don W. Jones, Jr.
Executive V.P. and Publisher: Robert W. Holland, Jr.
V.P., Design and Production: Anne Spencer
V.P., Manufacturing and Inventory Control: Therese Bräuer
Director, Sales and Marketing: William Kane
Editor-in-Chief, College: J. Michael Stranz
Production Manager: Amy Rose
Marketing Manager: Nathan Schultz
Associate Production Editor: Karen Ferreira
Editorial Assistant: Theresa DiDonato
Production Assistant: Jenny McIsaac
Cover Design: Night & Day Design
Composition: Northeast Compositors
Printing and Binding: Courier Westford
Cover Printing: John Pow Company
This book was typeset with Textures on a Macintosh G4. The font families used were Computer Modern and
Caslon. The first printing was printed on 50# Finch opaque.
Printed in the United States of America
06 05 04 03 02
10 9 8 7 6 5 4 3 2 1
For Dana, Kasey, and Cody
Contents
7.1
Contents
Preface
ix
Chapter 1.
Complex Numbers and the Complex Plane 1
1.1
Complex Numbers and Their Properties 2
1.2
Complex Plane 10
1.3
Polar Form of Complex Numbers 16
1.4
Powers and Roots 23
1.5
Sets of Points in the Complex Plane 29
1.6
Applications 36
Chapter 1 Review Quiz 45
Complex Functions and Mappings 49
2.1
Complex Functions 50
2.2
Complex Functions as Mappings 58
2.3
Linear Mappings 68
2.4
Special Power Functions 80
2.4.1
The Power Function
z
n
81
2.4.2
The Power Function
z
1/n
86
2.5
Reciprocal Function 100
2.6
Limits and Continuity 110
2.6.1
Limits 110
2.6.2
Continuity 119
2.7
Applications 132
Chapter 2 Review Quiz 138
Analytic Functions 141
3.1
Differentiability and Analyticity 142
3.2
Cauchy-Riemann Equations 152
3.3
Harmonic Functions 159
3.4
Applications 164
Chapter 3 Review Quiz 172
Chapter 2.
Chapter 3.
v

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