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Complex Analysis for Mathematics and Engineering

ISBN-10: 0763737488
ISBN-13: 9780763737481
Edition: 5th 2006 (Revised)
List price: $153.95
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Description: Complex Analysis for Mathematics and Engineering is intended for undergraduate students at the junior or senior undergraduate level majoring in mathematics, physics, or engineering. bull; bull;Complex Analysis bull;Complex Variables

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Book details

List price: $153.95
Edition: 5th
Copyright year: 2006
Publisher: Jones & Bartlett Learning, LLC
Publication date: 1/9/2006
Binding: Hardcover
Pages: 633
Size: 7.50" wide x 9.25" long x 1.50" tall
Weight: 3.256
Language: English

Complex Analysis for Mathematics and Engineering is intended for undergraduate students at the junior or senior undergraduate level majoring in mathematics, physics, or engineering. bull; bull;Complex Analysis bull;Complex Variables

Complex Numbers
The Origin of Complex Numbers
The Algebra of Complex Numbers
The Geometry of Complex Numbers
The Geometry of Complex Numbers, Continued
The Algebra of Complex Numbers, Revisited
The Topology of Complex Numbers
Complex Functions
Functions and Linear Mappings
The Mappings w = z[superscript n] and w = z[Characters not reproducible]
Limits and Continuity
Branches of Functions
The Reciprocal Transformation w = [Characters not reproducible]
Analytic and Harmonic Functions
Differentiable and Analytic Functions
The Cauchy-Riemann Equations
Harmonic Functions
Sequences, Julia and Mandelbrot Sets, and Power Series
Sequences and Series
Julia and Mandelbrot Sets
Geometric Series and Convergence Theorems
Power Series Functions
Elementary Functions
The Complex Exponential Function
The Complex Logarithm
Complex Exponents
Trigonometric and Hyperbolic Functions
Inverse Trigonometric and Hyperbolic Functions
Complex Integration
Complex Integrals
Contours and Contour Integrals
The Cauchy-Goursat Theorem
The Fundamental Theorems of Integration
Integral Representations for Analytic Functions
The Theorems of Morera and Liouville, and Extensions
Taylor and Laurent Series
Uniform Convergence
Taylor Series Representations
Laurent Series Representations
Singularities, Zeros, and Poles
Applications of Taylor and Laurent Series
Residue Theory
The Residue Theorem
Trigonometric Integrals
Improper Integrals of Rational Functions
Improper Integrals Involving Trigonometric Functions
Indented Contour Integrals
Integrands with Branch Points
The Argument Principle and Rouche's Theorem
z-Transforms and Applications
The z-Transform
Second-Order Homogeneous Difference Equations
Digital Signal Filters
Conformal Mapping
Basic Properties of Conformal Mappings
Bilinear Transformations
Mappings Involving Elementary Functions
Mapping by Trigonometric Functions
Applications of Harmonic Functions
Preliminaries
Invariance of Laplace's Equation and the Dirichlet Problem
Poisson's Integral Formula for the Upper Half-Plane
Two-Dimensional Mathematical Models
Steady State Temperatures
Two-Dimensional Electrostatics
Two-Dimensional Fluid Flow
The Joukowski Airfoil
The Schwarz-Christoffel Transformation
Image of a Fluid Flow
Sources and Sinks
Fourier Series and the Laplace Transform
Fourier Series
The Dirichlet Problem for the Unit Disk
Vibrations in Mechanical Systems
The Fourier Transform
The Laplace Transform
Laplace Transforms of Derivatives and Integrals
Shifting Theorems and the Step Function
Multiplication and Division by t
Inverting the Laplace Transform
Convolution
Answers
Index

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