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]
    Average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Materials specified Status Date due Barcode Course reserves
Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 34 Ar752 (Browse shelf) Available A-4071

ECUACIONES DIFERENCIALES


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)

There are no comments on this title.

to post a comment.

Click on an image to view it in the image viewer

¿Necesita ayuda?

Si necesita ayuda para encontrar información, puede visitar personalmente la biblioteca en Av. Alem 1253 Bahía Blanca, llamarnos por teléfono al 291 459 5116, o enviarnos un mensaje a biblioteca.antonio.monteiro@gmail.com

Powered by Koha