Functions of Complex Variables 复变函数论 第二版

　　马立新编著的这本《复变函数论（第2版）》共6 章，主要内容包括复数与复变函数、解析函数、 复变函数的积分、级数、留数及其应用和共形映射等 ，较全面、 系统地介绍了复变函数的基础知识。内容处理上重点 突出、叙述 简明，每节末附有适量习题供读者选用，适合高等师 范院校数学 系及普通综合性大学数学系高年级学生使用。

前言
Chapter I  Complex Numbers and Functions
  1  Complex Numbers
    1.1  Complex Number Field
    1.2  Complex Plane
    1.3  Modulus, Conjugation, Argument, Polar Representation
    1.4  Powers and Roots of Complex Numbers
    Exercises
  2  Regions in the Complex Plane
    2.1  Some Basic Concept
    2.2  Domain and Jordan Curve
    Exercises
  3  Functions of a Complex Variable
    3.1  The Concept of Functions of a Complex Variable
    3.2  Limits and Continuous
    Exercises
  4  The Extended Complex Plane and the Point at Infinity
    4.1  The Spherical Representation, the Extended Complex Plane
    4.2  Some Concepts in the Extended Complex Plane
    Exercises
Chapter II  Analytic Functions
  1  The Concept of the Analytic Function
    1.1  The Derivative of the Functions of a Complex Variable
    1.2  Analytic Functions
    Exercises
  2  Cauchy-Riemann Equations
    Exercises
  3  Elementary Functions
    3.1  The Exponential Function
    3.2  Trigonometric Functions
    3.3  Hyperbolic Functions
    Exercises
  4  Multi-Valued Functions
    4.1  The Logarithmic Function
    4.2  Complex Power Functions
    4. 3  Inverse Trigonometric and Hyperbolic Functions
    Exercises
Chapter III  Complex Integration
  1  The Concept of Contour Integrals
    1.1  Integral of a Complex Function over a Real Interval
    1.2  Contour Integrals
    Exercises
    Cauchy-Goursat Theorem
    2.1  Cauchy Theorem
    2.2  Cauchy Integral Formula
    2.3  Derivatives of Analytic Functions
    2.4  Liouville's Theorem and the Fundamental Theorem of Algebra
    Exercises
    Harmonic Functions
    Exercises
Chapter IV  Series
  1  Basic Properties of Series
    1.1  Convergence of Sequences
    1.2  Convergence of Series
    1.3  Uniform convergence
    Exercises
  2  Power Series
    Exercises
  3  Taylor Series
    Exercises
  4  Laurent Series
    Exercises
  5  Zeros of an Analytic Functions and Uniquely Determined Analytic
    Functions
    5.1  Zeros of Analytic Functions
    5.2  Uniquely Determined Analytic Functions
    5.3  Maximum Modulus Principle
    Exercises
  6  The Three Types of Isolated Singular Points at a Finite Point
    Exercises
  7  The Three Types of Isolated Singular Points at a Infinite Point
    Exercises
Chapter V  Calculus of Residues
  1  Residues
    1.1  Residues
    1.2  Cauchy's Residue Theorem
    1.3  The Calculus of Residue
    Exercises
  2  Applications of Residue
    2.1  The Type of Definite Integral □
    2.2  The Type of Improper Integral □
    2.3  The Type of Improper Integral □
    Exercises
  3  Argument Principle
    Exercises
Chapter VI  Conformal Mappings
  1  Analytic Transformation
    1.1  Preservation of Domains of Analytic Transformation
    1.2  Conformality of Analytic Transformation
    Exercises
  2  Rational Functions
    2.1  Polynomials
    2.2  Rational Functions
    Exercises
  3  Fractional Linear Transformations
    Exercises
  4  Elementary Conformal Mappings
    Exercises
  5  The Riemann Mapping Theorem
    Exercises
Appendix
  Appendix 1
  Appendix 2
Answers
Bibliography