An introduction to numerical analysis for electrical and computer engineers

605 Pages·2004·3.456 MB·English

by  Christopher J. Zarowski

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AN INTRODUCTION TO
NUMERICAL ANALYSIS
FOR ELECTRICAL AND
COMPUTER ENGINEERS
Christopher J. Zarowski
UniversityofAlberta,Canada
A JOHN WILEY & SONS, INC. PUBLICATION
TLFeBOOK
TLFeBOOK
AN INTRODUCTION TO
NUMERICAL ANALYSIS
FOR ELECTRICAL AND
COMPUTER ENGINEERS
TLFeBOOK
TLFeBOOK
AN INTRODUCTION TO
NUMERICAL ANALYSIS
FOR ELECTRICAL AND
COMPUTER ENGINEERS
Christopher J. Zarowski
UniversityofAlberta,Canada
A JOHN WILEY & SONS, INC. PUBLICATION
TLFeBOOK
Copyright(cid:1)c 2004byJohnWiley&Sons,Inc.Allrightsreserved.
PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.
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LibraryofCongressCataloging-in-PublicationData:
Zarowski,ChristopherJ.
Anintroductiontonumericalanalysisforelectricalandcomputerengineers/Christopher
J.Zarowski.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN0-471-46737-5(coth)
1.Electricengineering—Mathematics.2.Computerscience—Mathematics.3.Numerical
analysisI.Title.
TK153.Z372004
(cid:2) (cid:2)
621.301518—dc22
2003063761
PrintedintheUnitedStatesofAmerica.
10987654321
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Inmemoryofmymother
Lilian
andofmyfather
Walter
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CONTENTS
Preface xiii
1 Functional Analysis Ideas 1
1.1 Introduction 1
1.2 Some Sets 2
1.3 Some Special Mappings: Metrics, Norms, and Inner Products 4
1.3.1 Metrics and Metric Spaces 6
1.3.2 Norms and Normed Spaces 8
1.3.3 Inner Products and Inner Product Spaces 14
1.4 The Discrete Fourier Series (DFS) 25
Appendix 1.A Complex Arithmetic 28
Appendix 1.B Elementary Logic 31
References 32
Problems 33
2 Number Representations 38
2.1 Introduction 38
2.2 Fixed-Point Representations 38
2.3 Floating-Point Representations 42
2.4 Rounding Effects in Dot Product Computation 48
2.5 Machine Epsilon 53
Appendix 2.A Review of Binary Number Codes 54
References 59
Problems 59
3 Sequences and Series 63
3.1 Introduction 63
3.2 Cauchy Sequences and Complete Spaces 63
3.3 Pointwise Convergence and Uniform Convergence 70
3.4 Fourier Series 73
3.5 Taylor Series 78
vii
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