An Introduction To Numerical Analysis For Electrical And Computer Engineers

AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS Christopher J. Zarowski University of Alberta, Canada A JOHN WILEY & SONS, INC. PUBLICATION AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS Christopher J. Zarowski University of Alberta, Canada A JOHN WILEY & SONS, INC. PUBLICATION c 2004 by John Wiley & Sons, Inc. All rights reserved. Copyright Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the Web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services, please contact our Customer Care Department within the United States at 877-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Cataloging-in-Publication Data: Zarowski, Christopher J. An introduction to numerical analysis for electrical and computer engineers / Christopher J. Zarowski. p. cm. Includes bibliographical references and index. ISBN 0-471-46737-5 (coth) 1. Electric engineering—Mathematics. 2. Computer science—Mathematics. 3. Numerical analysis I. Title. TK153.Z37 2004 621.3 01 518—dc22 2003063761 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 In memory of my mother Lilian and of my father Walter CONTENTS Preface 1 2 3 xiii Functional Analysis Ideas 1 1.1 1.2 1.3 Introduction Some Sets Some Special Mappings: Metrics, Norms, and Inner Products 1.3.1 Metrics and Metric Spaces 1.3.2 Norms and Normed Spaces 1.3.3 Inner Products and Inner Product Spaces 1.4 The Discrete Fou