导语

  

内容提要

  

    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
Chapter 5 Review Quiz
Chapter S. Series and Residues
  6.1  Sequences and Series
  6.2  Taylor Series
  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 Real Improper Integrals
    6.6.3  Integration along a Branch Cut
    6.6.4  The Argument Principle and Rouch6's
Theorem
    6.6.5  Summing Infinite Series
  6.7  Applications
Chapter 6 Review Quiz
Chapter 7. Conformal Mappings
  7.1  Conformal Mapping
  7.2  Linear Fractional Transformations
  7.3  Schwarz-Christoffel Transformations
  7.4  Poisson Integral Formulas
  7.5  Applications
    7.5.1  Boundary-Value Problems
    7.5.2  Fluid Flow
Chapter 7 Review Quiz
Appendixes: I Proof of Theorem 3. I
II Proof of the Cauchy-Goursat Theorem
III Table of Conformal Mappings
Answers to Selected Odd-Numbered Problems
Symbol Index
Word Index