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偏微分方程 第1卷 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

偏微分方程 第1卷 英文
  • （德）索维尼著 著
  • 出版社： 世界图书出版公司北京公司
  • ISBN：7510035173
  • 出版时间：2011
  • 标注页数：442页
  • 文件大小：13MB
  • 文件页数：454页
  • 主题词：偏微分方程-教材-英文

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图书目录

Ⅰ Differentiation and Integration on Manifolds1

1 The Weierstraв approximation theorem2

2 Parameter-invariant integrals and differential forms12

3 The exterior derivative of differential forms23

4 The Stokes integral theorem for manifolds30

5 The integral theorems of Gauв and Stokes39

6 Curvilinear integrals56

7 The lemma of Poincaré67

8 Co-derivatives and the Laplace-Beltrami operator72

9 Some historical notices to chapter Ⅰ89

Ⅱ Foundations of Functional Analysis91

1 Daniell's integral with examples91

2 Extension of Daniell's integral to Lebesgue's integral96

3 Measurable sets109

4 Measurable functions121

5 Riemann's and Lebesgue's integral on rectangles134

6 Banach and Hilbert spaces140

7 The Lebesgue spaces Lp（X）151

8 Bounded linear functionals on Lp（X） and weak convergence161

9 Some historical notices to chapter Ⅱ172

Ⅲ Brouwer's Degree of Mapping with Geometric Applications175

1 The winding number175

2 The degree of mapping in In184

3 Geometric existence theorems193

4 The index of a mapping195

5 The product theorem204

6 Theorems of Jordan-Brouwer210

Ⅳ Generalized Analytic Functions215

1 The Cauchy-Riemann differential equation215

2 Holomorphic functions in Cn219

3 Geometric behavior of holomorphic functions in C233

4 Isolated singularities and the general residue theorem242

5 The inhomogeneous Cauchy-Riemann differential equation255

6 Pseudoholomorphic functions266

7 Conformal mappings270

8 Boundary behavior of conformal mappings285

9 Some historical notices to chapter Ⅳ295

Ⅴ Potential Theory and Spherical Harmonics297

1 Poisson's differential equation in Rn297

2 Poisson's integral formula with applications310

3 Dirichlet's problem for the Laplace equation in Rn321

4 Theory of spherical harmonics: Fourier series334

5 Theory of spherical harmonics in n variables340

Ⅵ Linear Partial Differential Equations in 1n355

1 The maximum principle for elliptic differential equations355

2 Quasilinear elliptic differential equations365

3 The heat equation370

4 Characteristic surfaces384

5 The wave equation in Rn for n＝1,3,2395

6 The wave equation in Rn forn≥2403

7 The inhomogeneous wave equation and an initial-boundary-value problem414

8 Classification, transformation and reduction of partial differential equations419

9 Some historical notices to the chapters Ⅳ and Ⅵ428

References431

Index433

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