复分析pdf电子书版本下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快] 温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页 直链下载[便捷但速度慢]   [在线试读本书]   [在线获取解压码]

复分析PDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

FIRST PART 1

Chapter Ⅰ The Complex Plane and Elementary Functions 1

1. Complex Numbers 1

2. Polar Representation 5

3. Stereographic Projection 11

4. The Square and Square Root Functions 15

5. The Exponential Function 19

6. The Logarithm Function 21

7. Power Functions and Phase Factors 24

8. Trigonometric and Hyperbolic Functions 29

Chapter Ⅱ Analytic Functions 33

1. Review of Basic Analysis 33

2. Analytic Functions 42

3. The Cauchy-Riemann Equations 46

4. Inverse Mappings and the Jacobian 51

5. Harmonic Functions 54

6. Conformal Mappings 58

7. Fractional Linear Transformations 63

Chapter Ⅲ Line Integrals and Harmonic Functions 70

1. Line Integrals and Green's Theorem 70

2. Independence of Path 76

3. Harmonic Conjugates 83

4. The Mean Value Property 85

5. The Maximum Principle 87

6. Applications to Fluid Dynamics 90

7. Other Applications to Physics 97

Chapter Ⅳ Complex Integration and Analyticity 102

1. Complex Line Integrals 102

2. Fundamental Theorem of Calculus for Analytic Functions 107

3. Cauchy's Theorem 110

4. The Cauchy Integral Formula 113

5. Liouville's Theorem 117

6. Morera's Theorem 119

7. Goursat's Theorem 123

8. Complex Notation and Pompeiu's Formula 124

Chapter Ⅴ Power Series 130

1. Infinite Series 130

2. Sequences and Series of Functions 133

3. Power Series 138

4. Power Series Expansion of an Analytic Function 144

5. Power Series Expansion at Infinity 149

6. Manipulation of Power Series 151

7. The Zeros of an Analytic Function 154

8. Analytic Continuation 158

Chapter Ⅵ Laurent Series and Isolated Singularities 165

1. The Laurent Decomposition 165

2. Isolated Singularities of an Analytic Function 171

3. Isolated Singularity at Infinity 178

4. Partial Fractions Decomposition 179

5. Periodic Functions 182

6. Fourier Series 186

Chapter Ⅶ The Residue Calculus 195

1. The Residue Theorem 195

2. Integrals Featuring Rational Functions 199

3. Integrals of Trigonometric Functions 203

4. Integrands with Branch Points 206

5. Fractional Residues 209

6. Principal Values 212

7. Jordan's Lemma 216

8. Exterior Domains 219

SECOND PART 224

Chapter Ⅷ The Logarithmic Integral 224

1. The Argument Principle 224

2. Rouche's Theorem 229

3. Hurwitz's Theorem 231

4. Open Mapping and Inverse Function Theorems 232

5. Critical Points 236

6. Winding Numbers 242

7. The Jump Theorem for Cauchy Integrals 246

8. Simply Connected Domains 252

Chapter Ⅸ The Schwarz Lemma and Hyperbolic Geometry 260

1. The Schwarz Lemma 260

2. Conformal Self-Maps of the Unit Disk 263

3. Hyperbolic Geometry 266

Chapter Ⅹ Harmonic Functions and the Reflection Principle 274

1. The Poisson Integral Formula 274

2. Characterization of Harmonic Functions 280

3. The Schwarz Reflection Principle 282

Chapter Ⅺ Conformal Mapping 289

1. Mappings to the Unit Disk and Upper Half-Plane 289

2. The Riemann Mapping Theorem 294

3. The Schwarz-Christoffel Formula 296

4. Return to Fluid Dynamics 304

5. Compactness of Families of Functions 306

6. Proof of the Riemann Mapping Theorem 311

THIRD PART 315

Chapter Ⅻ Compact Families of Meromorphic Functions 315

1. Marty's Theorem 315

2. Theorems of Montel and Picard 320

3. Julia Sets 324

4. Connectedness of Julia Sets 333

5. The Mandelbrot Set 338

Chapter ⅩⅢ Approximation Theorems 342

1. Runge's Theorem 342

2. The Mittag-Leffler Theorem 348

3. Infinite Products 352

4. The Weierstrass Product Theorem 358

Chapter ⅩⅣ Some Special Functions 361

1. The Gamma Function 361

2. Laplace Transforms 365

3. The Zeta Function 370

4. Dirichlet Series 376

5. The Prime Number Theorem 382

Chapter ⅩⅤ The Dirichlet Problem 390

1. Green's Formulae 390

2. Subharmonic Functions 394

3. Compactness of Families of Harmonic Functions 398

4. The Perron Method 402

5. The Riemann Mapping Theorem Revisited 406

6. Green's Function for Domains with Analytic Boundary 407

7. Green's Function for General Domains 413

Chapter ⅩⅥ Riemann Surfaces 418

1. Abstract Riemann Surfaces 418

2. Harmonic Functions on a Riemann Surface 426

3. Green's Function of a Surface 429

4. Symmetry of Green's Function 434

5. Bipolar Green's Function 436

6. The Uniformization Theorem 438

7. Covering Surfaces 441

Hints and Solutions for Selected Exercises 447

References 469

List of Symbols 471

Index 473