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Complex Variables: A Physical Approach with Applications and MATLAB

Steven G. Krantz
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2008
Number of Pages: 
421
Format: 
Hardcover
Series: 
Textbooks in Mathematics
Price: 
99.95
ISBN: 
9781584885801
Category: 
Textbook
We do not plan to review this book.

 PREFACE

BASIC IDEAS
Complex Arithmetic
Algebraic and Geometric Properties
The Exponential and Applications

HOLOMORPHIC AND HARMONIC FUNCTIONS
Holomorphic Functions
Holomorphic and Harmonic Functions
Real and Complex Line Integrals
Complex Differentiability
The Logarithm

THE CAUCHY THEORY
The Cauchy Integral Theorem
Variants of the Cauchy Formula
The Limitations of the Cauchy Formula

APPLICATIONS OF THE CAUCHY THEORY
The Derivatives of a Holomorphic Function
The Zeros of a Holomorphic Function

ISOLATED SINGULARITIES
Behavior near an Isolated Singularity
Expansion around Singular Points
Examples of Laurent Expansions
The Calculus of Residues
Applications to the Calculation of Integrals
Meromorphic Functions

THE ARGUMENT PRINCIPLE
Counting Zeros and Poles
Local Geometry of Functions
Further Results on Zeros
The Maximum Principle
The Schwarz Lemma

THE GEOMETRIC THEORY
The Idea of a Conformal Mapping
Mappings of the Disc
Linear Fractional Transformations
The Riemann Mapping Theorem
Conformal Mappings of Annuli
A Compendium of Useful Conformal Mappings

APPLICATIONS OF CONFORMAL MAPPING
Conformal Mapping
The Dirichlet Problem
Physical Examples
Numerical Techniques

HARMONIC FUNCTIONS
Basic Properties of Harmonic Functions
The Mean Value Property
The Poisson Integral Formula

TRANSFORM THEORY
Introductory Remarks
Fourier Series
The Fourier Transform
The Laplace Transform
A Table of Laplace Transforms
The z-Transform

PDES AND BOUNDARY VALUE PROBLEMS
Fourier Methods

COMPUTER PACKAGES
Introductory Remarks
The Software Packages

APPENDICES
Solutions to Odd-Numbered Exercises
Glossary of Terms
List of Notation
A Guide to the Literature

BIBLIOGRAPHY

INDEX

Dummy View - NOT TO BE DELETED