《復變函數引論》以解析函數為主線安排了復數及復數域與擴充復平面、復變函數與解析函數、初等解析函數、復變函數沿有向曲線的積分、級數、奇點與留數、留數應用共八章內容，從微分、積分、級數、在一點處、在一個收斂點列、在一個區域中等九個層次來逐步深入地展開對解析函數的討論，並利用解析函數的留數定理來計算一元實變函數的積分。本書對多值函數、解析函數等內容作了較好的處理，使傳統內容以全新的面貌出現。為方便讀者使用，各節配有適量的習題及必要的提示或解答。全書由曹麗霞負責組織各章節內容的討論和定稿。

《復變函數引論》是大學數學、信息與計算科學 等相關專業復變函數雙語(英語)教學用書，正文部分 均以英語陳述。 全書以解析函數為主線安排了復數及復數域與擴 充復平面、復變函數與解析函數、初等解析函數、復 變函數沿有向曲線的積分、級數、奇點與留數、留數 應用共八章內容，從微分、積分、級數、在一點處、 在一個收斂點列、在一個區域中等九個層次來逐步深 入地展開對解析函數的討論，並利用解析函數的留數 定理來計算一元實變函數的積分。本書對多值函數、 解析函數等內容作了較好的處理，使傳統內容以全新 的面貌出現。為方便讀者使用，各節配有適量的習題 及必要的提示或解答。 《復變函數引論》可作為數學專業本科生的雙語 教材或教學參考書，也可供大、中專數學教師、科技 工作者、工程技術人員及自學者參考。全書由曹麗霞 負責組織各章節內容的討論和定稿。

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
參考文獻