Ordinary differential equations /
Arnolʹd, V. I. 1937-2010
Ordinary differential equations / Vladimir I. Arnold ; translated from the Russian by Richard A. Silverman - First edition - vii, 280 pages : illustrations ; 24 cm.
Translation of: Obyknovennye differentsialʹnye uravneniya
Includes bibliographical references and index.
Basic concepts -- Basic theorems -- Linear systems -- Proofs of the basic theorems -- Differential equations on manifolds.
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).
9780262510189 (pbk) 0262510189 (pbk)
Differential equations
Ecuaciones diferenciales
515.352
Ordinary differential equations / Vladimir I. Arnold ; translated from the Russian by Richard A. Silverman - First edition - vii, 280 pages : illustrations ; 24 cm.
Translation of: Obyknovennye differentsialʹnye uravneniya
Includes bibliographical references and index.
Basic concepts -- Basic theorems -- Linear systems -- Proofs of the basic theorems -- Differential equations on manifolds.
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).
9780262510189 (pbk) 0262510189 (pbk)
Differential equations
Ecuaciones diferenciales
515.352