复变函数引论 mobi 下载 网盘 caj lrf pdf txt 阿里云

　　曹怀信编著的《复变函数引论(第2版)》简介：For several years, I have been

conducting courses in Complex Analysis, Real Analysis and

Functional Analysis in a so-called "bilingual" way. That is, the

less*** are given with Chinese textbooks, but mainly teached in

English. The main purpose of teaching in this way is to improve the

undergraduate students' ability to read and write English. Using a

Chinese textbook in such "bilingual" courses is not, however,

useful for training students' ability of English-thinking.

C***equently, although there are a number of books on complex

***ysis in Chinese, in order to meet the requirements of bilingual

teaching, it is necessary to write a textbook on complex ***ysis

in English for Chinese undergraduate students. This is just the

main aim of compiling the present book.

Preface

Chapter Ⅰ Complex Number Field

1.1 Sums and Products

1.2 Basic Algebraic Properties

1.3 Further Properties

1.4 Moduli

1.5 Conjugates

1.6 Exponential Form

1.7 Products and Quotients in Exponential Form

1.8 Roots of Complex Numbers

1.9 Examples

1.10 Regi*** in the Complex Plane

Chapter Ⅱ Analytic Functi***

2.1 Functi*** of a Complex Variable

2.2 Mappings

2.3 The Exponential Function and its Mapping Properties

2.4 Limits

2.5 Theorems on Limits

2.6 Limits Involving the Point at Infinity

2.7 Continuity

2.8 Derivatives

2.9 Differentiation Formulas

2.10 Cauchy-Riemann Equati***

2.11 Necessary and Sufficient Conditi*** for Differentiability

2.12 Polar Coordinates

2.13 Analytic Functi***

2.14 Examples

215 Harmonic Functi***

Chapter Ⅲ Elementary Functi***

3.1 The Exponential Function

3.2 The Logarithmic Function

3.3 Branches and Derivatives of Logarithms

3.4 Some Identities on Logarithms

3.5 Complex Power Functi***

36 Trigonometric Functi***

3.7 Hyperbolic Functi***

3.8 Inverse Trigonometric and Hyperbolic Functi***

Chapter Ⅳ Integrals

4.1 Derivatives of Complex-Valued Functi*** of One Real Variable

4.2 Definite Integrals of Functi*** W

4.3 Paths

4.4 Path Integrals

4.5 Examples

4.6 Upper Bounds for Integrals

4.7 Primitive Functi***

4.8 Examples

4.9 Cauchy Integral Theorem

4.10 Proof of the Cauchy Integral Theorem

4.11 Extended Cauchy Integral Theorem

4.12 Cauchy Integral Formula

4.13 Derivatives of Analytic Functi***

4.14 Liouville's Theorem

4.15 Maximum Modulus Principle

Chapter Ⅴ Series

5.1 Convergence of Series

5.2 Taylor Series

5.3 Examples

5.4 Laurent Series

5.5 Examples

5.6 Absolute and Uniform Convergence of Power Series

5.7 Continuity of Sums of Power Series

5.8 Integration and Differentiation of Power Series

5.9 Uniqueness of Series Representati***

5.10 Multiplication and Division of Power Series

Chapter Ⅵ Residues and Poles

6.1 Residues

6.2 Cauchy's Residue Theorem

6.3 Using a Single Residue

*** The Three Types of Isolated Singular Points

6.5 Residues at poles

6.6 Examples

6.7 Zeros of Analytic Functi***

6.8 Uniquely Determined Analytic Functi***

6.9 Zeros and Poles

6.10 Behavior of f Near Isolated Singular Points

6.11 Reflection Principle

Chapter Ⅶ Applicati*** of Residues

7 I Evaluation of Improper Integrals

7.2 Examples

7.3 Improper Integrals From Fourier Analysis

7.4 Jordan's Lemma

7.5 Indented Paths

7.6 An Indentation Around a Branch Point

7.7 Definite Integrals Involving Sine and Cosine

7.8 Argument Principle

7.9 Rouche's Theorem

Chapter Ⅷ Conformal Mappings

8.1 Conformal mappings

82 Unila***l Functi***

8.3 Local Inverses

84 Affine Transformati***

85 The Transformation W = 1/z

8.6 Mappings by 1/z

8.7 Fractional Linear Transformati***

8.8 Cross Ratios

8.9 Mappings of the Upper Half Plane

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