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Part 1 book “Complex analysis for mathematics and engineering” has contents: Complex numbers, complex functions, analytic and harmonic functions, sequences, series, and julia and mandelbrot sets, elementary functions, complex integration, taylor and laurent series. | Page iii Complex Analysis for Mathematics and Engineering Third Edition John H. Mathews California State UniversityFullerton Russell W. Howell Westmont College Page iv World Headquarters Jones and Bartlett Publishers 40 Tall Pine Drive Sudbury, MA 01776 978-443-5000 info@jbpub.com www.jbpub.com Jones and Bartlett Publishers Canada P.O. Box 19020 Toronto, ON M55 1X1 CANADA Jones and Bartlett Publishers International Barb House, Barb Mews London W6 7PA UK Copyright ©1997 by Jones and Bartlett Publishers. © 1996 Times Mirror Higher Education Group. Inc. All rights reserved. No 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, without permission in writing from the publisher. Library of Congress Catalog Number: 95-76589 ISBN 0-7637-0270-6 Printed in the United States of America 00 99 10 9 8 7 6 5 4 3 Page v Contents Preface ix Chapter 1 Complex Numbers 1 1.1 The Origin of Complex Numbers 1.2 The Algebra of Complex Numbers 1.3 The Geometry of Complex Numbers 1.4 The Geometry of Complex Numbers, Continued 1.5 The Algebra of Complex Numbers, Revisited 1.6 The Topology of Complex Numbers Chapter 2 Complex Functions 2.1 Functions of a Complex Variable 2.2 Transformations and Linear Mappings 2.3 The Mappings w = zn and w = z1/n 2.4 Limits and Continuity 2.5 Branches of Functions 2.6 The Reciprocal Transformation w = 1/z (Prerequisite for Section 9.2) Chapter 3 Analytic and Harmonic Functions 3.1 Differentiable Functions 3.2 The Cauchy-Riemann Equations 1 5 12 18 24 30 38 38 41 47 53 60 64 71 71 76 3.3 Analytic Functions and Harmonic Functions Chapter 4 Sequences, Series, and Julia and Mandelbrot Sets 4.1 Definitions and Basic Theorems for Sequences and Series 4.2 Power Series Functions 4.3 Julia and Mandelbrot .
