本书是21世纪高等院校教材，是一本用于同名课程双语教学的英文教材，内容分两部分，共8章，第一部分为复变函数部分，包括复数与复变函数、解析函数、复积分、级数、留数、保形映射；第二部分是积分变换部分，包括傅里叶变换和拉普拉斯变换。本书既可作为理工科大学同名课程的双语教材，也可供有关工程技术人员参考。

本书是一本用于同名课程双语教学的英文教材，编者参考多本有关的经典原著英文教材，按照国家教育部对本课程的基本要求，结合多年的教学实践编撰而成。内容分两部分，共8章，第1～6章为复变函数部分，包括complex numbers and functions of a complex variable(复数与复变函数)，analvtic functions(解析函数)，complex integrals(复积分)，series(级数)，residues(留数)，conformal mappings(保形映射)。第7章和第8章是积分变换部分，包括Foutier transform(傅里叶变换)和Laplace transfom(拉普拉斯变换)。书中各章节都安排了足够量的例题，在每章后也安排了大量精选的习题，并按大纲的要求及难易程度分为A、B两类。

本书既可作为理工科大学同名课程的双语教材，也可供有关工程技术人员参考。

Contents

Chapter 1 Complex Nnmhers and Functions of a Complex Variable

1.1 Complex numbers and its four fundamental operations

1.2 Geometric representation of complex numbers

1.3 Complex conjugates

1.4 Powers and roots

1.5 Riemann sphere and infinity

1.6 Complex number sets

1.7 Functions of a complex variable

Exercise 1

Chapter 2 Analytic Ftmctions

2.1 The concept of analytic function

2.2 Necessary and sufficient conditions of analytic functions

2.3 Elementary functions

Exercise 2

Chapter 3 Complex Integrals

3.1 The concept of complex integral

3.2 Cauchy integrM theorem

3.3 Cauchy integral formula

3.4 Analytic functions and harmonic functions

Exercise 3

Chapter 4 Series

4.1 Series of complex numbers and series of complex functions

4.2 Power series

4.3 Taylor series

 4.4 Laurent series

 Exercise 4

Chapter 5 Residues

 5.1 Isolated singularities

 5.2 Residues

 5.3 Application of residues in evaluating definite and improper integrals

Exercise 5

Chapter 6 Conformal Mappings

 6.1 The concept of conformal mapping

6.2 Fractional linear transformations

6.3 Condition of uniqueness

6.4 Some important fractional linear transformations

6.5 Mapping by some elementary functions

Exercise 6

Chapter 7 Fourier Transform

7.1 Fourier integral and Fourier integral theorem

7.2 Fourier transform and inverse Fourier transform

7.3 Unit impulse functions

7.4 Generalized 'Fourier transform

7.5 The properties of Fourier transform

7.6 Convolution

Exercise 7

Chapter 8 Laplace Transform

8.1 The concept of Laplace transform

8.2 The properties of Laplace transform

8.3 Inverse Laplace transform

8.4 Application of Laplace transform

Exercise 8.

Answers to Selected Exercises

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Bibliography

Appendix

Appendix A Table of Fourier transform

Appendix B Table of Laplace transform

Index