《复变函数引论》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。本书对多值函数、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。全书由曹丽霞负责组织各章节内容的讨论和定稿。

《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。本书对多值函数、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。

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

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