Ordinary differential equations / V. I. Arnold ; translated and edited by Richard A. Silverman.

Por: Arnol´d, V. I. (Vladimir Igorevich), 1937-Colaborador(es): Silverman, Richard A [trl, edt]Idioma: Inglés Lenguaje original: Ruso Editor: Cambridge, Mass. : MIT Press, c1973Descripción: viii, 280 p. : il. ; 24 cmISBN: 0262010372Títulos uniformes: Obyknovennye differentsial´nye uravneniia. Inglés Otra clasificación: 34-01 (34Cxx 37-01)
Contenidos:
Preface vii
Frequently Used Notation ix
1 Basic Concepts [1]
1 Phase Spaces and Phase Flows [1]
2 Vector Fields on the Line [11]
3 Phase Flows on the Line [19]
4 Vector Fields and Phase Flows in the Plane [24]
5 Nonautonomous Equations [28]
6 The Tangent Space [33]
2 Basic Theorems [48]
7 The Vector Field near a Nonsingular Point [48]
8 Applications to the Nonautonomous Case [56]
9 Applications to Equations of Higher Order [59]
10 Phase Curves of Autonomous Systems [68]
11 The Directional Derivative. First Integrals [72]
12 Conservative Systems with One Degree of Freedom [79]
3 Linear Systems [95]
13 Linear Problems [95]
14 The Exponential of an Operator [97]
15 Properties of the Exponential [104]
16 The Determinant of the Exponential [111]
17 The Case of Distinct Real Eigenvalues [115]
18 Complexification and Decomplexification [119]
19 Linear Equations with a Complex Phase Space [124]
20 Complexification of a Real Linear Equation [129]
21 Classification of Singular Points of Linear Systems [139]
22 Topological Classification of Singular Points [143]
23 Stability of Equilibrium Positions [154]
24 The Case of Purely Imaginary Eigenvalues [160]
25 The Case of Multiple Eigenvalues [167]
26 More on Quasi-Polynomials [176]
27 Nonautonomous Linear Equations [188]
28 Linear Equations with Periodic Coefficients [199]
29 Variation of Constants [208]
4 Proofs of the Basic Theorems [211]
30 Contraction Mappings [211]
31 The Existence, Uniqueness, and Continuity Theorems [213]
32 The Differentiability Theorem [223]
5 Differential Equations on Manifolds [233]
33 Differentiable Manifolds [233]
34 The Tangent Bundle. Vector Fields on a Manifold [243]
35 The Phase Flow Determined by a Vector Field [250]
36 The Index of a Singular Point of a Vector Field [254]
Sample Examination Problems [269]
Bibliography [273]
Index [275]
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Libros ordenados por tema 34 Ar752 (Browse shelf) Available A-4071

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Libros ordenados por tema 34 Ar752 (Browse shelf) ej. 2 Available A-9400

Traducción de: Obyknovennye differentsial´nye uravneniia, 1971.

Bibliografía: p. [273].

Preface vii --
Frequently Used Notation ix --
1 Basic Concepts [1] --
1 Phase Spaces and Phase Flows [1] --
2 Vector Fields on the Line [11] --
3 Phase Flows on the Line [19] --
4 Vector Fields and Phase Flows in the Plane [24] --
5 Nonautonomous Equations [28] --
6 The Tangent Space [33] --
2 Basic Theorems [48] --
7 The Vector Field near a Nonsingular Point [48] --
8 Applications to the Nonautonomous Case [56] --
9 Applications to Equations of Higher Order [59] --
10 Phase Curves of Autonomous Systems [68] --
11 The Directional Derivative. First Integrals [72] --
12 Conservative Systems with One Degree of Freedom [79] --
3 Linear Systems [95] --
13 Linear Problems [95] --
14 The Exponential of an Operator [97] --
15 Properties of the Exponential [104] --
16 The Determinant of the Exponential [111] --
17 The Case of Distinct Real Eigenvalues [115] --
18 Complexification and Decomplexification [119] --
19 Linear Equations with a Complex Phase Space [124] --
20 Complexification of a Real Linear Equation [129] --
21 Classification of Singular Points of Linear Systems [139] --
22 Topological Classification of Singular Points [143] --
23 Stability of Equilibrium Positions [154] --
24 The Case of Purely Imaginary Eigenvalues [160] --
25 The Case of Multiple Eigenvalues [167] --
26 More on Quasi-Polynomials [176] --
27 Nonautonomous Linear Equations [188] --
28 Linear Equations with Periodic Coefficients [199] --
29 Variation of Constants [208] --
4 Proofs of the Basic Theorems [211] --
30 Contraction Mappings [211] --
31 The Existence, Uniqueness, and Continuity Theorems [213] --
32 The Differentiability Theorem [223] --
5 Differential Equations on Manifolds [233] --
33 Differentiable Manifolds [233] --
34 The Tangent Bundle. Vector Fields on a Manifold [243] --
35 The Phase Flow Determined by a Vector Field [250] --
36 The Index of a Singular Point of a Vector Field [254] --
Sample Examination Problems [269] --
Bibliography [273] --
Index [275] --

MR, 50 #13677 (para la ed. original en ruso)

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