Applied Complex Variable

Häftad, Engelska, 2003

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Beskrivning

First half of this highly-regarded book covers complex number plane; functions and limits; Riemann surfaces, the definite integral; power series; meromorphic functions, and much more. The second half deals with potential theory; ordinary differential equations; Fourier transforms; Laplace transforms and asymptotic expansion. Exercises included.

Produktinformation

Utgivningsdatum:2003-03-28
Mått:138 x 215 x 25 mm
Vikt:625 g
Format:Häftad
Språk:Engelska
Serie:Dover Books on MaTHEMA 1.4tics
Antal sidor:512
Förlag:Dover Publications Inc.
ISBN:9780486646701

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Innehållsförteckning

Part I. Analytic Function TheoryChapter 1. The Complex Number Plane1.1 Introduction1.2 Complex Numbers1.3 The Complex Plane1.4 Point Sets in the Plane1.5 Stereographic Projection. The Extended Complex Plane1.6 Curves and RegionsChapter 2. Functions of a Complex Variable2.1 Functions and Limits2.2 Differentiability and Analyticity2.3 The Cauchy-Riemann Conditions2.4 Linear Fractional Transformations2.5 Transcendental functions2.6 Riemann SurfacesChapter 3. Integration in the Complex Plane3.1 Line Integrals3.2 The Definite Integral3.3 Cauchy's Theorem3.4 Implications of Cauchy's Theorem3.5 Functions Defined by Integration3.6 Cauchy Formulas3.7 Maximum Modulus PrincipleChapter 4. Sequences and Series4.1 Sequences of Complex Numbers4.2 Sequences of Complex Functions4.3 Infinite Series4.4 Power Series4.5 Analytic Continuation4.6 Laurent Series4.7 Double Series4.8 Infinite Products4.9 Improper Integrals4.10 The Gamma FunctionChapter 5. Residue Calculus5.1 The Residue Theorem5.2 Evaluation of Real Integrals5.3 The Principle of the Argument5.4 Meromorphic Functions5.5 Entire FunctionsPart II. Applications of Analytic Function TheoryChapter 6. Potential Theory6.1 Laplace's Equation in Physics6.2 The Dirichlet Problem6.3 Green's Functions6.4 Conformal Mapping6.5 The Schwarz-Christoffel Transformation6.6 Flows with Sources and Sinks6.7 Volume and Surface Distributions6.8 Singular Integral EquationsChapter 7. Ordinary Differential Equations7.1 Separation of Variables7.2 Existence and Uniqueness Theorems7.3 Solution of a Linear Second-Order Differential Equation Near an Ordinary Point7.4 Solution of a Linear Second-Order Differential Equation Near a Regular Singular Point7.5 Bessel Functions7.6 Legendre Functions7.7 Sturm-Liouville Problems7.8 Fredholm Integral EquationsChapter 8. Fourier Transforms8.1 Fourier Series8.2 The Fourier Integral Theorem8.3 The Complex Fourier Transform8.4 Properties of the Fourier Transform8.5 The Solution of Ordinary Differential Equations8.6 The Solution of Partial Differential Equations8.7 The Solution of Integral EquationsChapter 9. Laplace Transforms9.1 From Fourier to Laplace Transform9.2 Properties of the Laplace Transform9.3 Inversion of Laplace Transforms9.4 The Solution of Ordinary Differential Equations9.5 Stability9.6 The Solution of Partial Differential Equations9.7 The Solution of Integral EquationsChapter 10. Asymptotic Expansions10.1 Introduction and Definitions10.2 Operations on Asymptotic Expansions10.3 Asymptotic Expansion of Integrals10.4 Asymptotic Solutions of Ordinary Differential EquationsReferences; Index