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

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 Phase Spaces and Phase Flows 
2 Vector Fields on the Line 
3 Phase Flows on the Line 
4 Vector Fields and Phase Flows in the Plane 
5 Nonautonomous Equations 
6 The Tangent Space 
2 Basic Theorems 
7 The Vector Field near a Nonsingular Point 
8 Applications to the Nonautonomous Case 
9 Applications to Equations of Higher Order 
10 Phase Curves of Autonomous Systems 
11 The Directional Derivative. First Integrals 
12 Conservative Systems with One Degree of Freedom 
3 Linear Systems 
13 Linear Problems 
14 The Exponential of an Operator 
15 Properties of the Exponential 
16 The Determinant of the Exponential 
17 The Case of Distinct Real Eigenvalues 
18 Complexification and Decomplexification 
19 Linear Equations with a Complex Phase Space 
20 Complexification of a Real Linear Equation 
21 Classification of Singular Points of Linear Systems 
22 Topological Classification of Singular Points 
23 Stability of Equilibrium Positions 
24 The Case of Purely Imaginary Eigenvalues 
25 The Case of Multiple Eigenvalues 
26 More on Quasi-Polynomials 
27 Nonautonomous Linear Equations 
28 Linear Equations with Periodic Coefficients 
29 Variation of Constants 
4 Proofs of the Basic Theorems 
30 Contraction Mappings 
31 The Existence, Uniqueness, and Continuity Theorems 
32 The Differentiability Theorem 
5 Differential Equations on Manifolds 
33 Differentiable Manifolds 
34 The Tangent Bundle. Vector Fields on a Manifold 
35 The Phase Flow Determined by a Vector Field 
36 The Index of a Singular Point of a Vector Field 
Sample Examination Problems 
Bibliography 
Index ``` Average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Materials specified Copy number Status Date due Barcode Course reserves Libros
Libros ordenados por tema 34 Ar752 (Browse shelf) Available A-4071 Libros
Libros ordenados por tema 34 Ar752 (Browse shelf) ej. 2 Available A-9400
##### Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Libros ordenados por tema Close shelf browser
 34 Am513 Nonlinear ordinary differential equations in transport processes / 34 An532 Análisis no lineal / 34 An575 Theory of oscillators / 34 Ar752 Ordinary differential equations / 34 Ar752 Ordinary differential equations / 34 Ay985 Schaum's outline of theory and problems of differential equations / 34 B154 Nonlinear two point boundary value problems /

Traducción de: Obyknovennye differentsial´nye uravneniia, 1971.

Bibliografía: p. .

Preface vii --
Frequently Used Notation ix --
1 Basic Concepts  --
1 Phase Spaces and Phase Flows  --
2 Vector Fields on the Line  --
3 Phase Flows on the Line  --
4 Vector Fields and Phase Flows in the Plane  --
5 Nonautonomous Equations  --
6 The Tangent Space  --
2 Basic Theorems  --
7 The Vector Field near a Nonsingular Point  --
8 Applications to the Nonautonomous Case  --
9 Applications to Equations of Higher Order  --
10 Phase Curves of Autonomous Systems  --
11 The Directional Derivative. First Integrals  --
12 Conservative Systems with One Degree of Freedom  --
3 Linear Systems  --
13 Linear Problems  --
14 The Exponential of an Operator  --
15 Properties of the Exponential  --
16 The Determinant of the Exponential  --
17 The Case of Distinct Real Eigenvalues  --
18 Complexification and Decomplexification  --
19 Linear Equations with a Complex Phase Space  --
20 Complexification of a Real Linear Equation  --
21 Classification of Singular Points of Linear Systems  --
22 Topological Classification of Singular Points  --
23 Stability of Equilibrium Positions  --
24 The Case of Purely Imaginary Eigenvalues  --
25 The Case of Multiple Eigenvalues  --
26 More on Quasi-Polynomials  --
27 Nonautonomous Linear Equations  --
28 Linear Equations with Periodic Coefficients  --
29 Variation of Constants  --
4 Proofs of the Basic Theorems  --
30 Contraction Mappings  --
31 The Existence, Uniqueness, and Continuity Theorems  --
32 The Differentiability Theorem  --
5 Differential Equations on Manifolds  --
33 Differentiable Manifolds  --
34 The Tangent Bundle. Vector Fields on a Manifold  --
35 The Phase Flow Determined by a Vector Field  --
36 The Index of a Singular Point of a Vector Field  --
Sample Examination Problems  --
Bibliography  --
Index  --

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

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