The Resource Ordinary differential equations, [by] V. I. Arnold. Translated and edited by Richard A. Silverman
Ordinary differential equations, [by] V. I. Arnold. Translated and edited by Richard A. Silverman
Resource Information
The item Ordinary differential equations, [by] V. I. Arnold. Translated and edited by Richard A. Silverman represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Ordinary differential equations, [by] V. I. Arnold. Translated and edited by Richard A. Silverman represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- Summary
- 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
- Language
-
- eng
- rus
- eng
- Extent
- viii, 280 pages
- Note
- Translation of Obyknovennye differen︠t︡sialʹnye uravneni︠ia︡
- Contents
-
- Basic concepts
- Basic theorems
- Linear systems
- Proofs of the basic theorems
- Differential equations on manifolds
- Isbn
- 9780262010375
- Label
- Ordinary differential equations
- Title
- Ordinary differential equations
- Statement of responsibility
- [by] V. I. Arnold. Translated and edited by Richard A. Silverman
- Language
-
- eng
- rus
- eng
- Summary
- 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
- Cataloging source
- DLC
- http://library.link/vocab/creatorDate
- 1937-2010
- http://library.link/vocab/creatorName
- Arnolʹd, V. I.
- Illustrations
- illustrations
- Index
- index present
- Literary form
- non fiction
- http://library.link/vocab/subjectName
-
- Differential equations
- Equations différentielles
- Équations différentielles
- Gewone differentiaalvergelijkingen
- Gewöhnliche Differentialgleichung
- Label
- Ordinary differential equations, [by] V. I. Arnold. Translated and edited by Richard A. Silverman
- Note
- Translation of Obyknovennye differen︠t︡sialʹnye uravneni︠ia︡
- Bibliography note
- Bibliography: page [273]
- Carrier category
- volume
- Carrier category code
-
- nc
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- Basic concepts -- Basic theorems -- Linear systems -- Proofs of the basic theorems -- Differential equations on manifolds
- Control code
- 624013
- Dimensions
- 23 cm
- Extent
- viii, 280 pages
- Isbn
- 9780262010375
- Lccn
- 73006846
- Media category
- unmediated
- Media MARC source
- rdamedia
- Media type code
-
- n
- Other physical details
- illustrations
- System control number
- (WaOLN)618821
- Label
- Ordinary differential equations, [by] V. I. Arnold. Translated and edited by Richard A. Silverman
- Note
- Translation of Obyknovennye differen︠t︡sialʹnye uravneni︠ia︡
- Bibliography note
- Bibliography: page [273]
- Carrier category
- volume
- Carrier category code
-
- nc
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- Basic concepts -- Basic theorems -- Linear systems -- Proofs of the basic theorems -- Differential equations on manifolds
- Control code
- 624013
- Dimensions
- 23 cm
- Extent
- viii, 280 pages
- Isbn
- 9780262010375
- Lccn
- 73006846
- Media category
- unmediated
- Media MARC source
- rdamedia
- Media type code
-
- n
- Other physical details
- illustrations
- System control number
- (WaOLN)618821
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Ordinary-differential-equations-by-V.-I./Y0Ugx045VzQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Ordinary-differential-equations-by-V.-I./Y0Ugx045VzQ/">Ordinary differential equations, [by] V. I. Arnold. Translated and edited by Richard A. Silverman</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
