Rent 9780070084964 | Complex Variables and Applications | Brown, James Ward; Churchill, Ruel Vance @knetbooks.com

Summary Table of Contents

This text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserves the basic content and style of earlier editions and includes many new and relevant applications which are introduced early in the text.

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Preface
Complex Numbers
Sums and Products
Algebraic Properties
Moduli and Conjugates
Triangle Inequality
Polar Coordinates and Euler's Formula
Products and Quotients in Exponential Form
Roots of Complex Numbers
Regions in the Complex Plane
Analytic Functions
Functions of a Complex Variable
Mappings
Limits
Theorems on Limits
Limits Involving the Point at Infinity
Continuity
Derivatives
Differential Formulas
Cauchy-Riemann Equations
Sufficient Conditions for Differentiability
Polar Coordinates
Analytic Functions
Reflection Principle
Harmonic Functions
Elementary Functions
The Exponential Function
Trigonometric Functions
Hyperbolic Functions
The Logarithmic Function and Its Branches
Some Identities Involving Logarithms
Complex Exponents
Inverse Trigonometric and Hyperbolic Functions
Integrals
Complex-Valued Functions w(t)
Contours
Contour Integrals
Examples
Antiderivatives
Examples
Cauchy-Goursat Theorem
Proof of the Theorem
Simply and Multiply Connected Domains
Cauchy Integral Formula
Derivatives of Analytic Functions
Liouville's Theorem and the Fundamental Theorem of Algebra
Maximum Moduli of Functions
Series
Convergence of Sequences and Series
Taylor Series
Examples
Laurent Series
Examples
Absolute and Uniform Convergence of Power Series
Integration and Differentiation of Power Series
Uniqueness of Series Representations
Multiplication and Division of Power Series
Analytic Continuation
Residues and Poles
Residues
Residue Theorems
The Three Types of Isolated Singular Points
Residues at Poles
Zeros and Poles of Order m
Conditions under Which f (z) = 0
Behavior of f Near Removable and Essential Singular Points
Applications of Residues
Evaluation of Improper Integrals
Improper Integrals Involving Sines and Cosines
Definite Integrals Involving Sines and Cosines
Indented Paths
Integration along a Branch Cut
Argument Principle and Rouche's Theorem
Inverse Laplace Transforms
Examples
Mapping by Elementary Functions
Linear Transformations
The Transformation w = 1/z
Linear Fractional Transformations
An Implicit Form
Mapping of the Upper Half Plane
Exponential and Logarithmic Transformations
The Transformation w = sin z
Mappings by Branches of z 1/2
Square Roots of Polynomials
Riemann Surfaces
Surfaces for Related Functions
Conformal Mapping
Preservation of Angles
Further Properties
Harmonic Conjugates
Transformations of Harmonic Functions
Transformations of Boundary Conditions
Applications of Conformal Mapping
Steady Temperatures
Steady Temperatures in a Half Plane
A Related Problem
Temperatures in a Quadrant
Electrostatic Potential
Potential in a Cylindrical Space
Two-Dimensional Fluid Flow
The Stream Function
Flows around a Corner and around a Cylinder
The Schwartz-Christoffel Transformation
Mapping the Real Axis onto a Polygon
Schwarz-Christoffel Transformation
Triangles and Rectangles
Degenerate Polygons
Fluid Flow in a Channel through a Slit
Flow in a Channel with an Offset
Electrostatic Potential about an Edge of a Conducting Plate
Integral Formulas of the Poisson Type
Poisson Integral Formula
Dirichlet Problem for a Disk
Related Boundary Value Problems
Schwarz Integral Formula
Dirichlet Problem for a Half Plane
Neumann Problem for a Disk
Neumann Problem for a Half Plane
Appendixes
Bibliography
Table of Transformations of Regions
Index
Table of Contents provided by Publisher. All Rights Reserved.

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