复分析及其应用初级教程（第3版）

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。

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

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。

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