复变函数引论
作 者： 曹丽霞，罗英语，仲光苹 编
出版时间：2013
丛编项： 学者书屋系列
内容简介
《学者书屋系列：复变函数引论》是大学数学、信息与计算科学等相关专业复变函数双语（英语）教学用书，正文部分均以英语陈述。全书以解析函数为主线安排了复数及复数域与扩充复平面、复变函数与解析函数、初等解析函数、复变函数沿有向曲线的积分、级数、奇点与留数、留数应用共八章内容，从微分、积分、级数、在一点处、在一个收敛点列、在一个区域中等九个层次来逐步深入地展开对解析函数的讨论，并利用解析函数的留数定理来计算一元实变函数的积分。《学者书屋系列：复变函数引论》对多值函数、解析函数等内容作了较好的处理，使传统内容以全新的面貌出现。为方便读者使用，各节配有适量的习题及必要的提示或解答。《复变函数引论》可作为数学专业本科生的双语教材或教学参考书，也可供大、中专数学教师、科技工作者、工程技术人员及自学者参考。全书由曹丽霞负责组织各章节内容的讨论和定稿。
目录
Chapter 1 Complex Numbers
1.1 Complex Numbers
Exercises for 1.1
Answers or Hints for Exercises 1.1
1.2 Moduli and Conjugates
Exercises for 1.2
Answers or Hints for Exercises 1.2
1.3 Exponential Form
Exercises for 1.3
Answers or Hints for Exercises 1.3
1.4 Powers and Roots
Exercises for 1.4
Answers or Hints for Exercises 1.4
1.5 Geometrically Application of Complex Numbers
Exercises for 1.5
1.6 Plane Topology
Exercises for 1.6
Answers or Hints for Exercises 1.6
1.7 Curves
Chapter 2 Analytic Functions
2.1 Complex-valued Functions of a Complex Variable
Exercises for 2.1
Answers or Hints for Exercises 2.1
2.2 Limits and Continuity
Exercises for 2.2
Answers or Hints for Exercises 2.2
2.3 The Extended Plane and Infinity
Exercises for 2.3
Answers or Hints for Exercises 2.3
2.4 Complex Differentiability
Exercises for 2.4
Answers or Hints for Exercises 2.4
2.5 Analytic Functions
Exercises for 2.5
Answers or Hints for Exercises 2.5
2.6 Laplace's Equation and Harmonic Conjugates
Exercises for 2.6
Answers or Hints for Exercises 2.6
Chapter 3 Elementary Functions
3.1 The Exponential Functions
Exercises for 3.1
Answers or Hints for Exercises 3.1
3.2 Linear Fractional Transformations
Exercises for 3.2
Answers or Hints for Exercises 3.2
3.3 Trigonometric Functions
Exercises for 3.3
Answers or Hints for Exercises 3.3
3.4 The Radical Functions
Exercises for 3.4
Answers or Hints for Exercises 3.4
3.5 The Logarithm Function
Exercises for 3.5
Answers or Hints for Exercises 3.5
3.6 Complex Exponents
Exercises for 3.6
Answers or Hints for Exercises 3.6
3.7 Inverse Trigonometric and Hyperbolic Functions
Exercises for 3.7
Answers or Hints for Exercises 3.7
Chapter 4 Complex Integrals
4.1 Contour Integrals and Its Simple Properties
Exercise for 4.1
Answers or Hints for Exercises 4.1
4.2 Antiderivatives
Exercises for 4.2
Answers or Hints for Exercises 4.2
4.3 Cauchy Theorem
Exercises for 4.3
Answers or Hints for Exercises 4.3
4.4 Cauchy Integral Formula
Exercises for 4.4
Answers or Hints for Exercises 4.4
4.5 Maximum Modulus Principle
Exercises for 4.5
Answers or Hints for Exercises 4.5
Chapter 5 Power Series
5.1 Complex Sequences， Series and Their Basic Properties
Exercises for 5.1
Answers or Hints for Exercises 5.1
5.2 Series of Complex Functions and Its Basic Properties
Exercises for 5.2
Answers or Hints for Exercises 5.2
5.3 Power Series
Exercises for 5“. 3
Answers or Hints for Exercises 5.3
5.4 Taylor Series for Analytic Functions
Exercises for 5.4 ~
Answers or Hints for Exercises 5.4
5.5 Manipulation of Power Series
Exercises for 5.5
Answers or Hints for Exercises 5.5
5.6 The Zeros of Analytic Functions
Exercises for 5.6
Answers or Hints for Exercises 5.6
Chapter 6 Laurent Series and Isolated Singularities
6.1 Lanrent Decomposition
Exercises for 6.1
Answers or Hints for Exercises 6.1
6.2 Isolated Singular Point and Its Types
Exercises for 6.2
Answers or Hints for Exercises 6.2
6.3 Isolated Singularity at Infinity
Exercises for 6.3
Answers or Hints for Exercises 6.3
6.4 Entire Functions and Meromorphic Functions
Exercises for 6.4
Answers or Hints for Exercises 6.4
Chapter 7 Residue
7.1 Residue and Cauchy Residue Theorem
Exercises for 7.1
Answers or Hints for Exercises 7.1
7.2 The Argument Principle， Rouche's Theorem
Exercises for 7.2
Answers or Hints for Exercises 7.2
Chapter 8 Evaluation of Real Integrals
8.1 Integrals of Trigonometric Functions
Exercises for 8.1
Answers or Hints for Exercises 8.1
8.2 Rational Functions over the Real Line
Exercises for 8.2
Answers or Hints for Exercises 8.2
8.3 Rational and Trigonometric Functions over the Real Line
Exercises for 8.3
Answers or Hints for Exercises 8.3
8.4 Principal Value Integrals， Indentation Round a Singularity
Exercises for 8.4
Answers or Hints for Exercises 8.4
8.5 Integrals with Branch Points
Exercises for 8.5
Answers or Hints for Exercises 8.5
参考文献
