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适读人群 ：本书可作为高等工科院校各专业本科生的复变函数与积分变换课程双语课程教材，也可供有关工程技术人员参考。
本书是哈尔滨工业大学复变函数与积分变换双语教材，具有课件，适合于双语教学。是学习复变函数与积分变换的有利工具书，配合主教材使用效果更佳。
内容简介
书籍
数学书籍
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），analytic 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Fourier transform（傅里叶变换）和Laplace transform（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。
数学书籍
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），analytic 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Fourier transform（傅里叶变换）和Laplace transform（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。
作译者
盖云英，女，教授，博士生指导教师，教学带头人；哈尔滨工业大学理学院数学系教授，现在已经退休，原来为哈尔滨工业大学复变函数与积分变换学科带头人。四十年教龄教师，教学经验丰富，出版畅销经典教材三部。
目录
Chapter 1 Complex Numbers 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 Functions
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 integral theorem
3.3 Cauchy integral formula
3.4 Analytic functions and harmonic functions
Exercise 3
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 Functions
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 integral theorem
3.3 Cauchy integral formula
3.4 Analytic functions and harmonic functions
Exercise 3
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以“双语化、分层次、立体化”为特点，融中英文双语、分层次纸质化教材，同步学习辅导，中、英文版教学课件、电子教案以及习题详解于一体的创新型系列化教材，适应普通高等教育不同层次学校学生学习使用.
书摘
Chapter 1 Complex Numbers and Functions of a Complex Variable
§1.1 Complex numbers and its four fundamental operations
1. Introduction to complex numbers
As early as the sixteenth century Girolamo Cardano (Italian, 1501-1576) considered quadratic (and cubic) equations such as , which is satisfied by no real number , for example . Cardano noticed that if these “complex numbers” were treated as ordinary numbers with the added rule that , they did indeed solve the equations.
The important expression is now given the widely accepted designation . (This convention is not followed by the electrical engineers who prefer the symbol since they wish to reserve the symbol for electric current)
It is customary to denote a complex number:
The real numbers and are known as the real and imaginary parts of , respectively, and we write Two complex numbers are equal whenever they have the same real parts and the same imaginary parts, and . In what sense are these complex numbers an extension of the real ? We have already said that if is a real, we also write to stand for a . In other words, we are this regarding the real numbers as those complex numbers , where . If in the expression the term , we call a pure imaginary number.
§1.1 Complex numbers and its four fundamental operations
1. Introduction to complex numbers
As early as the sixteenth century Girolamo Cardano (Italian, 1501-1576) considered quadratic (and cubic) equations such as , which is satisfied by no real number , for example . Cardano noticed that if these “complex numbers” were treated as ordinary numbers with the added rule that , they did indeed solve the equations.
The important expression is now given the widely accepted designation . (This convention is not followed by the electrical engineers who prefer the symbol since they wish to reserve the symbol for electric current)
It is customary to denote a complex number:
The real numbers and are known as the real and imaginary parts of , respectively, and we write Two complex numbers are equal whenever they have the same real parts and the same imaginary parts, and . In what sense are these complex numbers an extension of the real ? We have already said that if is a real, we also write to stand for a . In other words, we are this regarding the real numbers as those complex numbers , where . If in the expression the term , we call a pure imaginary number.
