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复变函数引论PDF|Epub|txt|kindle电子书版本网盘下载

曹丽霞，罗英语，仲光苹主编；高伟，田淑杰副主编著
出版社：哈尔滨：哈尔滨工程大学出版社
ISBN：9787566106469
出版时间：2013
标注页数：299页
文件大小：34MB
文件页数：309页
主题词：复变函数－高等学校－教材－英文

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图书目录

Chapter 1 Complex Numbers1

1.1 Complex Numbers1

Exercises for 1.15

Answers or Hints for Exercises 1.16

1.2 Moduli and Conjugates6

Exercises for 1.29

Answers or Hints for Exercises 1.210

1.3 Exponential Form10

Exercises for 1.313

Answers or Hints for Exercises 1.314

1.4 Powers and Roots14

Exercises for 1.417

Answers or Hints for Exercises 1.419

1.5 Geometrically Application of Complex Numbers20

Exercises for 1.523

1.6 Plane Topology23

Exercises for 1.625

Answers or Hints for Exercises 1.626

1.7 Curves27

Chapter 2 Analytic Functions30

2.1 Complex-valued Functions of a Complex Variable30

Exercises for 2.135

Answers or Hints for Exercises 2.137

2.2 Limits and Continuity37

Exercises for 2.243

Answers or Hints for Exercises 2.244

2.3 The Extended Plane and Infinity44

Exercises for 2.347

Answers or Hints for Exercises 2.347

2.4 Complex Differentiability48

Exercises for 2.454

Answers or Hints for Exercises 2.456

2.5 Analytic Functions57

Exercises for 2.560

Answers or Hints for Exercises 2.561

2.6 Laplace’ s Equation and Harmonic Conjugates62

Exercises for 2.666

Answers or Hints for Exercises 2.667

Chapter 3 Elementary Functions69

3.1 The Exponential Functions69

Exercises for 3.171

Answers or Hints for Exercises 3.172

3.2 Linear Fractional Transformations73

Exercises for 3.281

Answers or Hints for Exercises 3.282

3.3 Trigonometric Functions83

Exercises for 3.385

Answers or Hints for Exercises 3.387

3.4 The Radical Functions87

Exercises for 3.491

Answers or Hints for Exercises 3.492

3.5 The Logarithm Function92

Exercises for 3.595

Answers or Hints for Exercises 3.597

3.6 Complex Exponents97

Exercises for 3.6101

Answers or Hints for Exercises 3.6102

3.7 Inverse Trigonometric and Hyperbolic Functions103

Exercises for 3.7104

Answers or Hints for Exercises 3.7105

Chapter 4 Complex Integrals107

4.1 Contour Integrals and Its Simple Properties107

Exercise for 4.1114

Answers or Hints for Exercises 4.1117

4.2 Antiderivatives118

Exercises for 4.2124

Answers or Hints for Exercises 4.2126

4.3 Cauchy Theorem126

Exercises for 4.3134

Answers or Hints for Exercises 4.3135

4.4 Cauchy Integral Formula136

Exercises for 4.4146

Answers or Hints for Exercises 4.4148

4.5 Maximum Modulus Principle149

Exercises for 4.5153

Answers or Hints for Exercises 4.5153

Chapter 5 Power Series155

5.1 Complex Sequences， Series and Their Basic Properties155

Exercises for 5.1158

Answers or Hints for Exercises 5.1160

5.2 Series of Complex Functions and Its Basic Properties160

Exercises for 5.2165

Answers or Hints for Exercises 5.2166

5.3 Power Series167

Exercises for 5.3172

Answers or Hints for Exercises 5.3173

5.4 Taylor Series for Analytic Functions173

Exercises for 5.4180

Answers or Hints for Exercises 5.4183

5.5 Manipulation of Power Series184

Exercises for 5.5187

Answers or Hints for Exercises 5.5188

5.6 The Zeros of Analytic Functions189

Exercises for 5.6194

Answers or Hints for Exercises 5.6196

Chapter 6 Laurent Series and Isolated Singularities197

6.1 Laurent Decomposition197

Exercises for 6.1202

Answers or Hints for Exercises 6.1205

6.2 Isolated Singular Point and Its Types209

Exercises for 6.2221

Answers or Hints for Exercises 6.2223

6.3 Isolated Singularity at Infinity224

Exercises for 6.3228

Answers or Hints for Exercises 6.3228

6.4 Entire Functions and Meromorphic Functions230

Exercises for 6.4233

Answers or Hints for Exercises 6.4234

Chapter 7 Residue236

7.1 Residue and Cauchy Residue Theorem236

Exercises for 7.1244

Answers or Hints for Exercises 7.1246

7.2 The Argument Principle，Rouche’s Theorem247

Exercises for 7.2254

Answers or Hints for Exercises 7.2255

Chapter 8 Evaluation of Real Integrals257

8.1 Integrals of Trigonometric Functions257

Exercises for 8.1260

Answers or Hints for Exercises 8.1262

8.2 Rational Functions over the Real Line263

Exercises for 8.2268

Answers or Hints for Exercises 8.2270

8.3 Rational and Trigonometric Functions over the Real Line，272

Exercises for 8.3275

Answers or Hints for Exercises 8.3276

8.4 Principal Value Integrals，Indentation Round a Singularity277

Exercises for 8.4288

Answers or Hints for Exercises 8.4288

8.5 Integrals with Branch Points289

Exercises for 8.5297

Answers or Hints for Exercises 8.5297

参考文献299