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复分析引论大中专理科科技综合曹怀信等编新华正版

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作者曹怀信等编

出版社科学出版社

ISBN9787030603678

出版时间2019-02

版次1

装帧平装

开本16

页数228页

字数302千字

定价49元

货号xhwx_1201840540

上书时间2024-12-14

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品相描述：全新: 正版特价新书

商品描述: 目录：

preface
chapter 1 plex number field
1.1 addition and multiplication
1.2 basic algebraic properties
1.3 further properties
1.4 moduli of plex numbers
1.5 conjugates of plex numbers
1.6 arguments of plex numbers
1.7 arguments of products and quotients
1.8 roots of plex numbers
1.9 examples of roots
1.10 domains and regions in the plex ne
chapter 2 plex variable functions
2.1 plex variable functions
2.2 functions as mappings
2.3 the exponential function and its mapping properties
2.4 limits of sequences and functions
2.5 properties of limits
2.6 limits involving the infinity
2.7 continuous functions
2.8 differentiable functions
2.9 differentiation formulas
2.10 a characterization of differentiability
2.11 cauchy-piemann equations in polar coordinates
2.12 analytic functions
chapter 3 elementary functions
3.1 the exponential function
3.2 trigonometric functions
3.3 the logarithmic function
3.4 branches of logarithms
3.5 plex power functions
chapter 4 integral theory of plex functions
4.1 definite integrals
4.2 path integrals
4.3 putation and estimation of integrals
4.4 cauchy integral theorem and its extensions
4.5 proof of cauchy integral theorem
4.6 cauchy integral formula
4.7 cauchy integral formula for derivatives
4.8 liouvilles theorem and mamum modulus principle
chapter 5 taylor series and laurent series
5.1 convergence of series
5.2 taylor series
5.3 laurent series
5.4 absolute and uniform convergence of power series
5.5 properties of sums of power series
5.6 uniqueness of series representations
chapter 6 singular points and zeros of analytic functions.
6.1 singular points
6.2 behavior of a function near isolated singular points
6.3 residues of functions
6.4 zeros of analytic functions
6.5 zeros and poles
6.6 argument principle
6.7 rouches theorem
chapter 7 conformal mappings
7.1 concepts and examples
7.2 unilateral functions
7.3 local inverses
7.4 affine transformations
7.5 the reciprocal transformation
7.6 fractional linear transformations
7.7 cross ratios
7.8 mappings of the upper half ne
bibliography

内容简介：

本书是作者多年从事复变函数论双语经验的结。其内容设置适合我国现行高等院校(特别是师范院校)本科的目标与课时需要。本书内容深入浅出、层次分明，理论体系严谨、逻辑推导详尽，强调“分析式”法，在引入概念前，加入了必要的分析与归纳结，然后提出相应的概念；在提出问题之后，进行推理分析、增加条件，后得到问题的，并把前边的讨论结成一个定理。其次，本书配有大量图形，帮助读者直观理解相应的概念与论证思路。