复分析及其应用初级教程（第3版）简介，目录书摘

2019-10-30 10:09 来源：京东作者：京东

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内容简介:

本书主要面向有微积分基础的本科生，是一部全面介绍复分析的基本理论和应用的入门性教材，其中也以学生易于接受的方式讨论了许多相关数学论题。本书语言简单明了，以大量的例题、图表和应用实例清晰地阐明复分析概念。各章的大量习题和复分析在科学和工程领域中的应用实例，将有助于学生领会和掌握复分析的理论精髓。

作者简介:

本书的第1作者Dennis G. Zill，艾奥瓦州立大学应用数学博士，洛杉矶Loyola Marymount大学数学教授，其研究领域包括应用数学、特殊函数及积分变换。

Preface
Chapter 1． Complex Numbers and the Complex Plane
1．1 Complex Numbers and Their Properties
1．2 ComplexPlane
1．3 Polar Form of Complex Numbers
1．4 Powers and Roots
1．5 Sets of Points in the Complex Plane
1．6 Applications
Chapter 1 Review Quiz

Chapter 2． Complex Functions and Mappings
2．1 ComplexFunctions
2．2 Complex Functions as Mappings
2．3 LinearMappings
2．4 Special Power Functions
2．4．1 The Power Function Zn
2．4．2 The Power Function zl
2．5 ReciprocalFunction
2．6 Applications

Chapter 2 Review Quiz
Chapter 3． Analytic Functions
3．1 Limits and Continuity
3．1．1 Limits
3．1．2 Continuity
3．2 Differentiability and Analyticity
3．3 Cauchy-RiemannEquations
3．4 Harmonic Functions
3．5 Applications

Chapter 3 Review Quiz
Chapter 4． Elementary Functions
4．1 Exponential and Logarithmic Functions
4．1．1 Complex Exponential Function
4．1．2 Complex Logarithmic Function
4．2 Complex Powers
4．3 Trigonometric and Hyperbolic Functions
4．3．1 Complex Trigonometric Functions
4．3．2 Complex Hyperbolic Functions
4．4 Inverse Trigonometric and Hyperbolic Functions
4．5 Applications

Chapter4 Review Quiz
Chapter 5． Integration in the Complex Plane
5．1 Reallntegrals
5．2 Complexlntegrals
5．3 Cauchy-GoursatTheorem
5．4 Independence of Path
5．5 Cauchy's Integral Formulas and Their
Consequences
5．5．1 Cauchy's Twolntegral Formulas
5．5．2 Some Consequences of the Integral
Formulas
5．6 Applications

Chapter 5 Review Quiz
Chapter 6． Series and esidues
6．1 Sequences and Series
6．2 TaylorSeries
6．3 Laurent Series
6．4 Zeros and Poles
6．5 Residues and Residue Theorem
6．6 Some Consequences of the Residue Theorem
6．6．1 Evaluation of Real Trigonometric
Integrals
6．6．2 Evaluation of Reallmproperlntegrals
6．6．3 Integration along a Branch Cut
6．6．4 The Argument Principle and Rouche's
Theorem
6．6．5 Summing Infinite Series
6．7 Applications

Chapter 6 Review Quiz
Chapter 7． ConformaIMappings
7．1 ConformaIMapping
7．2 Linear Fractional Transformations
7．3 Schwarz-ChristoffeITransformations
7．4 Poisson Integral Formulas
7．5 Applications
7．5．1 Boundary-ValueProblems
7．5．2 Fluid Flow

Chapter 7 Review Quiz
Appendixes： I ProofofTheorem 3．1．1 APP
Ⅱ Proof of the Cauchy-Goursat Theorem APP
ni Table ofConformal Mappings APP
Answers to Selected Odd-Numbered Problems ANS
Symbollndex IND
Wordlndex IND