《ORDINARY DIFFERENTIAL EQUATIONS》

作者 V.I.ARNOLD 编者
出版 THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY
参考页数 280
出版时间 1973（求助前请核对）  目录预览
ISBN号 0262010372 — 求助条款
PDF编号 813666368（仅供预览，未存储实际文件）
求助格式 扫描PDF（若分多册发行，每次仅能受理1册）
ORDINARY DIFFERENTIAL EQUATIONS 1973 PDF电子版封面 0262010372 V.I.ARNOLD

1 Basic Concepts1

1 Phase Spaces and Phase Flows1

2 Vector Fields on the Line11

3 Phase Flows on the Line19

4 Vector Fields and Phase Flows in the Plane24

5 Nonautonomous Equations28

6 The Tangent Space33

2 Basic Theorems48

7 The Vector Field near a Nonsingular Point48

8 Applications to the Nonautonomous Case56

9 Applications to Equations of Higher Order59

10 Phase Curves of Autonomous Systems68

11 The Directional Derivative.First Integrals72

12 Conservative Systems with One Degree of Freedom79

3 Linear Systems95

13 Linear Problems95

14 The Exponential of an Operator97

15 Properties of the Exponential104

16 The Determinant of the Exponential111

17 The Case of Distinct Real Eigenvalues115

18 Complexification and Decomplexification119

19 Linear Equations with a Complex Phase Space124

20 Complexification of a Real Linear Equation129

21 Classification of Singular Points of Linear Systems139

22 Topological Classification of Singular Points143

23 Stability of Equilibrium Positions154

24 The Case of Purely Imaginary Eigenvalues160

25 The Case of Multiple Eigenvalues167

26 More on Quasi-Polynomials176

27 Nonautonomous Linear Equations188

28 Linear Equations with Periodic Coefficients199

29 Variation of Constants208

4 Proofs of the Basic Theorems211

30 Contraction Mappings211

31 The Existence, Uniqueness, and Continuity Theorems213

32 The Differentiability Theorem223

5 Differential Equationson Manifolds233

33 Differentiable Manifolds233

34 The Tangent Bundle.Vector Fields on a Manifold243

35 The Phase Flow Determined by a Vector Field250

36 The Index of a Singular Point of a Vector Field254

Sample Examination Problems269

Bibliography273

Index275

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