复变函数FunctionofComplexVariable数学和信息科学学院课件

1、复变函数Function of Complex Variable 数学与信息科学学院 Colledge of Mathematics and Information ScienceE-learningFunction of Complex VariableChapter I Complex number fieldChapter II Analytic FunctionsChapter III IntegralsChapter IV SeriesChapter V ResiduesChapter VI Conformal Mappings数系 Number SystemN :The set o

2、f all natural numbersZ :The set of all integersQ :The set of all rational numbersR :The set of all real numbersC :The set of all complex numbersi : imaginary numberNatural number systemChapter I Complex number field1.1 Complex numbersreal partimaginary partz is real number ;z is pure imaginary numbe

3、r . 1.2 Operation 运算Sums and products 和与乘积 1.2 Operation 运算交换律 Commutative law：结合律 Associative law：分配律 Distribution law：additive inverse 加法逆元multiplicative inverse 乘法逆元additive identity 加法单位元multiplicative identity Division 商1.3 Modulus and argument of z 复数的模和辅角模 Modulus of z :辅角 Argument of z :辅角的主

4、值 Principal value of Arg z :Ex 1:1.3 Modulus and argument of z 复数的模和辅角1.3 Modulus and argument of z 复数的模和辅角Triangle inequality 三角不等式The conjugate of z=x+iy is defined as x-iy , and is denoted by 1.4 Conjugate 共轭 1.4 Conjugate 共轭Ex 2: 1.5 Exponential form 复数的指数形式exponential form of z 1.5 Exponential

5、form 复数的指数形式Root of complex numberDe Moivres formulaEx 4: 1.5 Exponential form 复数的指数形式1.6 Regions in the complex plane-neighborhood of For any set a point is said to bean interior point of E, if an exterior point of E, if an boundary point of E, if : the set of all boundary point of E is called the

6、boundary of E.Ex 3 :thenOpen set : A set is open if and only if each of its points is an interior point.Closed set : A set is closed if and only ifotherwise, called isolated point of E.For any set , a point is said to bean accumulate point of E, if 1.6 Regions in the complex planeE is called connected if each pair of points and in it can be joined by a polygonal line, consisting of a finite number of line segments joined end to end, that lies entirely in E.Ex 4 :is neither open nor closed.C and are both open and closed.domain : A open set that is connected.region : A domain