Applied Complex Variables

ISBN-10: 048664670X
ISBN-13: 9780486646701
Edition: Reprint 
Authors: John W. Dettman
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Book details

List price: $19.95
Publisher: Dover Publications, Incorporated
Publication date: 6/17/2010
Binding: Paperback
Pages: 512
Size: 5.50" wide x 8.75" long x 1.00" tall
Weight: 1.100
Language: English

Analytic Function Theory
The Complex Number Plane
Introduction
Complex Numbers
The Complex Plane
Point Sets in the Plane
Stereographic Projection
The Extended Complex Plane
Curves and Regions
Functions of a Complex Variable
Functions and Limits
Differentiability and Analyticity
The Cauchy-Riemann Conditions
Linear Fractional Transformations
Transcendental functions
Riemann Surfaces
Integration in the Complex Plane
Line Integrals
The Definite Integral
Cauchy's Theorem
Implications of Cauchy's Theorem
Functions Defined by Integration
Cauchy Formulas
Maximum Modulus Principle
Sequences and Series
Sequences of Complex Numbers
Sequences of Complex Functions
Infinite Series
Power Series
Analytic Continuation
Laurent Series
Double Series
Infinite Products
Improper Integrals
The Gamma Function
Residue Calculus
The Residue Theorem
Evaluation of Real Integrals
The Principle of the Argument
Meromorphic Functions
Entire Functions
Applications of Analytic Function Theory
Potential Theory
Laplace's Equation in Physics
The Dirichlet Problem
Green's Functions
Conformal Mapping
The Schwarz-Christoffel Transformation
Flows with Sources and Sinks
Volume and Surface Distributions
Singular Integral Equations
Ordinary Differential Equations
Separation of Variables
Existence and Uniqueness Theorems
Solution of a Linear Second-Order Differential Equation Near an Ordinary Point
Solution of a Linear Second-Order Differential Equation Near a Regular Singular Point
Bessel Functions
Legendre Functions
Sturm-Liouville Problems
Fredholm Integral Equations
Fourier Transforms
Fourier Series
The Fourier Integral Theorem
The Complex Fourier Transform
Properties of the Fourier Transform
The Solution of Ordinary Differential Equations
The Solution of Partial Differential Equations
The Solution of Integral Equations
Laplace Transforms
From Fourier to Laplace Transform
Properties of the Laplace Transform
Inversion of Laplace Transforms
The Solution of Ordinary Differential Equations
Stability
The Solution of Partial Differential Equations
The Solution of Integral Equations
Asymptotic Expansions
Introduction and Definitions
Operations on Asymptotic Expansions
Asymptotic Expansion of Integrals
Asymptotic Solutions of Ordinary Differential Equations
References
Index

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