复分析及其应用初级教程(第3版)(英文版)

D.G.齐尔、P.D.沙纳汉著的《复分析及其应用 初级教程(第3版)(英文版)》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 Complex Plane 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 Complex Functions 2.2 Complex Functions as Mappings 2.3 Linear Mappings 2.4 Special Power Functions 2.4.1 The Power Function z 2.4.2 The Power Function zl 2.5 Reciprocal Function 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-Riemann Equations 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 Chapter 4 Review Quiz Chapter 5. Integration in the Complex Plane 5.1 Real Integrals 5.2 Complex Integrals 5.3 Cauchy-Goursat Theorem 5.4 Independence of Path 5.5 Cauchy's Integral Formulas and Their Consequences 5.5.1 Cauchy's Two Integral Formulas 5.5.2 Some Consequences of the Integral Formulas 5.6 Applications