Basic Complex Analysis,9780716728771

Basic Complex Analysis

by ;
Edition: 3rd
ISBN13: 9780716728771
ISBN10: 071672877X
Format: Hardcover
Pub. Date: 1998-12-15
Publisher(s): W. H. Freeman
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Summary

Basic Complex Analysisskillfully combines a clear exposition of core theory with a rich variety of applications. Designed for undergraduates in mathematics, the physical sciences, and engineering who have completed two years of calculus and are taking complex analysis for the first time. .

Table of Contents

Preface vii
Analytic Functions
1(94)
Introduction to Complex Numbers
1(11)
Properties of Complex Numbers
12(13)
Some Elementary Functions
25(16)
Continuous Functions
41(19)
Basic Properties of Analytic Functions
60(21)
Differentiation of the Elementary Functions
81(14)
Cauchy's Theorem
95(88)
Contour Integrals
95(16)
Cauchy's Theorem---A First Look
111(12)
A Closer Look at Cauchy's Theorem
123(21)
Cauchy's Integral Formula
144(20)
Maximum Modulus Theorem and Harmonic Functions
164(19)
Series Representation of Analytic Functions
183(60)
Convergent Series of Analytic Functions
184(19)
Power Series and Taylor's Theorem
203(19)
Laurent Series and Classification of Singularities
222(21)
Calculus of Residues
243(76)
Calculation of Residues
243(13)
Residue Theorem
256(13)
Evaluation of Definite Integrals
269(35)
Evaluation of Infinite Series and Partial-Fraction Expansions
304(15)
Conformal Mappings
319(46)
Basic Theory of Conformal Mappings
319(8)
Fractional Linear and Schwarz-Christoffel Transformations
327(18)
Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics
345(20)
Further Development of the Theory
365(44)
Analytic Continuation and Elementary Riemann Surfaces
365(19)
Rouche's Theorem and Principle of the Argument
384(14)
Mapping Properties of Analytic Functions
398(11)
Asymptotic Methods
409(48)
Infinite Products and the Gamma Function
409(18)
Asymptotic Expansions and the Method of Steepest Descent
427(19)
Stirling's Formula and Bessel Functions
446(11)
Laplace Transform and Applications
457(24)
Basic Properties of Laplace Transforms
457(14)
Complex Inversion Formula
471(5)
Application of Laplace Transforms to Ordinary Differential Equations
476(5)
Answers to Odd-Numbered Exercises 481(25)
Index 506

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