Complex Variables and Applications

ISBN-10: 0073051942
ISBN-13: 9780073051949
Edition: 8th 2009
List price: $223.33
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Description: These classic textbooks, specializing in the techniques and applications of advanced mathematics to physical science and engineering, have endured as perennial standards for more than 60 years. The latest editions preserve the hallmark features that  More...

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Book details

List price: $223.33
Edition: 8th
Copyright year: 2009
Publisher: McGraw-Hill Higher Education
Publication date: 1/10/2008
Binding: Hardcover
Pages: 480
Size: 6.75" wide x 9.25" long x 1.00" tall
Weight: 1.958
Language: English

These classic textbooks, specializing in the techniques and applications of advanced mathematics to physical science and engineering, have endured as perennial standards for more than 60 years. The latest editions preserve the hallmark features that made Brown and Churchill a household name in advanced mathematics education-clear and concise exposition, interesting examples, and accessible level-while adding new enhancements, improved organization, and more modern examples and applications to serve another generation of students.

Preface
Complex Numbers
Sums and Products
Basic Algebraic Properties
Further Properties
Vectors and Moduli
Complex Conjugates
Exponential Form
Products and Powers in Exponential Form
Arguments of Products and Quotients
Roots of Complex Numbers
Examples
Regions in the Complex Plane
Analytic Functions
Functions of a Complex Variable
Mappings
Mappings by the Exponential Function
Limits
Theorems on Limits
Limits Involving the Point at Infinity
Continuity
Derivatives
Differentiation Formulas
Cauchy-Riemann Equations
Sufficient Conditions for Differentiability
Polar Coordinates
Analytic Functions
Examples
Harmonic Functions
Uniquely Determined Analytic Functions
Reflection Principle
Elementary Functions
The Exponential Function
The Logarithmic Function
Branches and Derivatives of Logarithms
Some Identities Involving Logarithms
Complex Exponents
Trigonometric Functions
Hyperbolic Functions
Inverse Trigonometric and Hyperbolic Functions
Integrals
Derivatives of Functions w(t)
Definite Integrals of Functions w(t)
Contours
Contour Integrals
Some Examples
Examples with Branch Cuts
Upper Bounds for Moduli of Contour Integrals
Antiderivatives
Proof of the Theorem
Cauchy-Goursat Theorem
Proof of the Theorem
Simply Connected Domains
Multiply Connected Domains
Cauchy Integral Formula
An Extension of the Cauchy Integral Formula
Some Consequences of the Extension
Liouville's Theorem and the Fundamental Theorem of Algebra
Maximum Modulus Principle
Series
Convergence of Sequences
Convergence of Series
Taylor Series
Proof of Taylor's Theorem
Examples
Laurent Series
Proof of Laurent's Theorem
Examples
Absolute and Uniform Convergence of Power Series
Continuity of Sums of Power Series
Integration and Differentiation of Power Series
Uniqueness of Series Representations
Multiplication and Division of Power Series
Residues and Poles
Isolated Singular Points
Residues
Cauchy's Residue Theorem
Residue at Infinity
The Three Types of Isolated Singular Points
Residues at Poles
Examples
Zeros of Analytic Functions
Zeros and Poles
Behavior of Functions Near Isolated Singular Points
Applications of Residues
Evaluation of Improper Integrals
Example
Improper Integrals from Fourier Analysis
Jordan's Lemma
Indented Paths
An Indentation Around a Branch Point
Integration Along a Branch Cut
Definite Integrals Involving Sines and Cosines
Argument Principle
Rouche's Theorem
Inverse Laplace Transforms
Examples
Mapping by Elementary Functions
Linear Transformations
The Transformation w = 1/z
Mappings by 1/z
Linear Fractional Transformations
An Implicit Form
Mappings of the Upper Half Plane
The Transformation w = sin z
Mappings by z[superscript 2] and Branches of z[superscript 1/2]
Square Roots of Polynomials
Riemann Surfaces
Surfaces for Related Functions
Conformal Mapping
Preservation of Angles
Scale Factors
Local Inverses
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 Schwarz-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 Problems
Appendixes
Bibliography
Table of Transformations of Regions
Index

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