Basic Complex Analysis

ISBN-10: 071672877X
ISBN-13: 9780716728771
Edition: 3rd 1999 (Revised)
List price: $173.99
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Description: This respected text is designed for mathematicians, physical science and engineering students familiar with calculus, but new to complex analysis. The third edition had been revised to make it more accessible to the student.

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Book details

List price: $173.99
Edition: 3rd
Copyright year: 1999
Publisher: W. H. Freeman & Company
Publication date: 12/15/1998
Binding: Hardcover
Pages: 600
Size: 7.50" wide x 10.00" long x 1.25" tall
Weight: 2.288
Language: English

This respected text is designed for mathematicians, physical science and engineering students familiar with calculus, but new to complex analysis. The third edition had been revised to make it more accessible to the student.

Preface
Analytic Functions
Introduction to Complex Numbers
Properties of Complex Numbers
Some Elementary Functions
Continuous Functions
Basic Properties of Analytic Functions
Differentiation of the Elementary Functions
Cauchy's Theorem
Contour Integrals
Cauchy's Theorem--A First Look
A Closer Look at Cauchy's Theorem
Cauchy's Integral Formula
Maximum Modulus Theorem and Harmonic Functions
Series Representation of Analytic Functions
Convergent Series of Analytic Functions
Power Series and Taylor's Theorem
Laurent Series and Classification of Singularities
Calculus of Residues
Calculation of Residues
Residue Theorem
Evaluation of Definite Integrals
Evaluation of Infinite Series and Partial-Fraction Expansions
Conformal Mappings
Basic Theory of Conformal Mappings
Fractional Linear and Schwarz-Christoffel Transformations
Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics
Further Development of the Theory
Analytic Continuation and Elementary Riemann Surfaces
Rouche's Theorem and Principle of the Argument
Mapping Properties of Analytic Functions
Asymptotic Methods
Infinite Products and the Gamma Function
Asymptotic Expansions and the Method of Steepest Descent
Stirling's Formula and Bessel Functions
Laplace Transform and Applications
Basic Properties of Laplace Transforms
Complex Inversion Formula
Application of Laplace Transforms to Ordinary Differential Equations
Answers to Odd-Numbered Exercises
Index

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