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ORDINARY DIFFERENTIAL EQUATIONSPDF|Epub|txt|kindle电子书版本网盘下载
- V.I.ARNOLD 著
- 出版社： THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY
- ISBN：0262010372
- 出版时间：1973
- 标注页数：280页
- 文件大小：36MB
- 文件页数：289页
- 主题词：
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图书目录
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