عنوان

Ordinary differential equations /

(Number (ISBN

0262010372

(Number (ISBN

0262510189

(Number (ISBN

9780262010375

(Number (ISBN

9780262510189

Number

b736762

Title Proper

Ordinary differential equations /

General Material Designation

[Book]

First Statement of Responsibility

V.I. Arnold ; translated and edited by Richard A. Silverman.

Place of Publication, Distribution, etc.

[Cambridge] :

Name of Publisher, Distributor, etc.

[MIT Press],

Date of Publication, Distribution, etc.

[1973]

Specific Material Designation and Extent of Item

viii, 280 pages :

Other Physical Details

illustrations ;

Dimensions

23 cm

Text of Note

Translation of Obyknovennye different︠s︡ialʹnye uravnenii︠a︡.

Text of Note

Includes bibliographical references (page 273) and index.

Text of Note

Basic concepts -- Basic theorems -- Linear systems -- Proofs of the basic theorems -- Differential equations on manifolds.

0

Text of Note

Although there is no lack of other books on this subject, even with the same title, the appearance of this new one is fully justified on at least two grounds: its approach makes full use of modern mathematical concepts and terminology of considerable sophistication and abstraction, going well beyond the traditional presentation of the subject; and, at the same time, the resulting enhancement of mathematical abstractness is counterbalanced by a constant appeal to geometrical and physical considerations, presented in the main text and in numerous problems and exercises. In the terms of mathematical approach, the text is dominated by two central ideas: the theorem on rectifiability of a vector field (which is equivalent to the usual theorems on existence, uniqueness, and differentiability of solutions) and the theory of one-parameter groups of linear transformations (equivalent to the theory of linear autonomous systems). The book also develops whole congeries of fundamental concepts--like phase space and phase flows, smooth manifolds and tangent bundles, vector fields and one-parameter groups of diffeomorphisms--that remain in the shadows in the traditional coordinate-based approach. All of these concepts are presented in some detail, but without assuming any background on the part of the reader beyond the scope of the standard elementary courses on analysis and linear algebra.

Terms of Availability

£8.25

General Material Designation

Obyknovennye different︠s︡ialʹnye uravnenii︠a︡.

Language (when part of a heading)

English

Differential equations.

Équations différentielles

31.44 ordinary differential equations.

Differential equations.

Differential equations.

Equations différentielles.

Gewöhnliche Differentialgleichung

Gewone differentiaalvergelijkingen.

Number

513.72

Number

Class number

Book number

Class number

Class number

System Code

System Code

Arnolʹd, V. I., (Vladimir Igorevich),1937-2010.

Date of Transaction

20201203205125.0

Electronic name

[Book]

Y