图书介绍

PARTIAL DIFFERENTIAL EQUATIONSpdf电子书版本下载

PARTIAL DIFFERENTIAL EQUATIONS
  • 出版社:
  • ISBN:
  • 出版时间:未知
  • 标注页数:248页
  • 文件大小:10MB
  • 文件页数:256页
  • 主题词:

PDF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]

下载说明

PARTIAL DIFFERENTIAL EQUATIONSPDF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

图书目录

CHAPTER Ⅰ.DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS 1

1.1.Some definitions and examples 1

1.2.The classification of equations and their solutions 6

1.3.Power series solutions and existence theorems 12

1.4.Transformations of variables;tensors 20

CHAPTER Ⅱ.LINEAR EQUATIONS OF THE FIRST ORDER 24

2.1.Homogeneous linear equations 24

2.2.The quasi-linear equation of the first order 29

2.3.Systems of linear homogeneous equations 36

2.4.Adjoint systems 40

CHAPTER Ⅲ.NON-LINEAR EQUATIONS OF THE FIRST ORDER 47

3.1.Geometric theory of the characteristics 47

3.2.Complete integrals 55

3.3.The Hamilton-Jacobi theorem 58

3.4.Involutory systems 62

3.5.Jacobi's integration method 66

CHAPTER Ⅳ.LINEAR EQUATIONS OF THE SECOND ORDER 70

4.1.Classification;the fundamental tensor 71

4.2.Riemannian geometry 74

4.3.Green's formula 80

4.4.Flat space.Equations with constant coefficients 84

4.5.Geodesics and geodesic distance 88

CHAPTER Ⅴ.SELF-ADJOINT ELLIPTIC EQUATIONS 98

5.1.The Dirichlet integral 99

5.2.A maximum principle 102

5.3.The local fundamental solution 104

5.4.Volume and surface potentials 110

5.5.Closed Riemannian spaces 116

5.6.The formulation of boundary value problems 120

CHAPTER Ⅵ.LINEAR INTEGRAL-EQUATIONS 125

6.1.Fredholm's first theorem 125

6.2.Fredholm's second theorem 130

6.3.Fredholm's third theorem 133

6.4.Iterated kernels 135

6.5.Symmetric kernels 140

6.6.Eigenfunction expansions 144

CHAPTER Ⅶ.BOUNDARY VALUE PROBLEMS 147

7.1.Poisson'a equation and the fundamental solution in the large 147

7.2.Solution of the boundary value problems 151

7.3.Representation formulae 156

7.4.The kernel function 162

CHAPTER Ⅷ.EIGENFUNCTIONS 169

8.1.Harmonic functions 169

8.2.Harmonic domain functionals 173

8.3.The Poisson equation in a closed space 177

8.4.Dirichlet's problem for the Poisson equation 182

8.5.Eigenfunction expansions 185

8.6.Initial value problems 190

CHAPTER Ⅸ.NORMAL HYPERBOLIC EQUATIONS 195

9.1.Characteristic surfaces 195

9.2.Bicharacteristies 200

9.3.Discontinuities and singularities 205

9.4.The propagation of waves 208

9.5.The initial value problem 212

CHAPTER Ⅹ.INTEGRATION OF THE WAVE EQUATION 217

10.1.The Riemann-Liouville integral 217

10.2.The fractional hyperbolic potential 220

10.3.The Cauchy problem 224

10.4.Verification of the solution 226

10.5.Lorentz spaces of even dimension 233

10.6.Lorentz spaces of odd dimension 236

10.7.The equation in a Riemann space 238

BIBLIOGRAPHY 244

INDEX 246

精品推荐