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常微分方程2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

常微分方程
  • W.WALTER编 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7506259281
  • 出版时间：2003
  • 标注页数：380页
  • 文件大小：95MB
  • 文件页数：398页
  • 主题词：微积分

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图书目录

Introduction1

Chapter Ⅰ．First Order Equations:Some Integrable Cases9

1．Explicit First Order Equations9

2．The Linear Differential Equation.Related Equations27

Supplement:The Generalized Logistic Equation33

3．Differential Equations for Families of Curves.Exact Equations36

4．Implicit First Order Differential Equations46

Chapter Ⅱ:Theory of First Order Differential Equations53

5．Tools from Functional Analysis53

6．An Existence and Uniqueness Theorem62

Supplement:Singular Initial Value Problems70

7．The Peano Existence Theorem73

Supplement:Methods of Functional Analysis80

8．Complex Differential Equations.Power Series Expansions83

9．Upper and Lower Solutions.Maximal and Minimal Integrals89

Supplement:The Separatrix98

Chapter Ⅲ:First Order Systems.Equations of Higher Order105

10．The Initial Value Problem for a System of First Order105

Supplement Ⅰ:Differential Inequalities and Invariance111

Supplement Ⅱ:Differential Equations in the Sense of Carathéodory121

11．Initial Value Problems for Equations of Higher Order125

Supplement:Second Order Differential Inequalities139

12．Continuous Dependence of Solutions141

Supplement:General Uniqueness and Dependence Theorems146

13．Dependence of Solutions on Initial Values and Parameters148

Chapter Ⅳ:Linear Differential Equations159

14．Linear Systems159

15．Homogeneous Linear Systems164

16．Inhomogeneous Systems170

Supplement:L1-Estimation of C-Solutions173

17．Systems with Constant Coefficients175

18．Matrix Functions.Inhomogeneous Systems190

Supplement:Floquet Theory195

19．Linear Differential Equations of Order n198

20．Linear Equations of Order n with Constant Coefficients204

Supplement:Linear Differential Equations with Periodic Coefficients210

Chapter Ⅴ:Complex Linear Systems213

21．Homogeneous Linear Systems in the Regular Case213

22．Isolated Singularities216

23．Weakly Singular Points.Equations of Fuchsian Type222

24．Series Expansion of Solutions225

25．Second Order Linear Equations236

Chapter Ⅵ:Boundary Value and Eigenvalue Problems245

26．Boundary Value Problems245

Supplement Ⅰ:Maximum and Minimum Principles260

Supplement Ⅱ:Nonlinear Boundary Value Problems262

27．The Sturm-Liouville Eigenvalue Problem268

Supplement:Rotation-Symmetric Elliptic Problems281

28．Compact Self-Adjoint Operators in Hilbert Space286

Chapter Ⅶ:Stability and Asymptotic Behavior305

29．Stability305

30．The Method of Lyapunov318

Appendix333

A．Topology333

B．Real Analysis342

C．Complex Analysis348

D．Functional Analysis350

Solutions and Hints for Selected Exercises357

Literature367

Index372

Notation379

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