Ordinary Differential Equations | Taschenbuch

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Cover: 9783540345633 | Ordinary Differential Equations | Vladimir I. Arnold | Taschenbuch

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Sprache: Englisch

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Beschreibung

The first two chapters of this book have been thoroughly revised and sig nificantly expanded. Sections have been added on elementary methods of in tegration (on homogeneous and inhomogeneous first-order linear equations and on homogeneous and quasi-homogeneous equations), on first-order linear and quasi-linear partial differential equations, on equations not solved for the derivative, and on Sturm's theorems on the zeros of second-order linear equa tions. Thus the new edition contains all the questions of the current syllabus in the theory of ordinary differential equations. In discussing special devices for integration the author has tried through out to lay bare the geometric essence of the methods being studied and to show how these methods work in applications, especially in mechanics. Thus to solve an inhomogeneous linear equation we introduce the delta-function and calculate the retarded Green's function; quasi-homogeneous equations lead to the theory of similarity and the law of universal gravitation, while the theorem on differentiability of the solution with respect to the initial conditions leads to the study of the relative motion of celestial bodies in neighboring orbits. The author has permitted himself to include some historical digressions in this preface. Differential equations were invented by Newton (1642-1727).

Zusammenfassung

Arnol'd's ODE book distinguishes itself from the dozens of others by its emphasis on the qualitative and geometric theory rather than the quantitative theory. His aim is to analyze and describe the behavior of systems, rather than providing a collection of unexplained tricks for solving specific equations. Thus, there are plenty of examples and figures, but no complicated formulas. Arnol'd is known by mathematicians and students both for his mathematical skills and for his talent for mathematical writing.

Erscheinungsjahr:	2006
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	344
Reihe:	Universitext
Inhalt:	iv 338 S. 272 s/w Illustr. 338 p. 272 illus.
ISBN-13:	9783540345633
ISBN-10:	3540345639
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Arnold, Vladimir I.
Übersetzung:	Cooke, R.
Auflage:	1st ed 1992. 2nd printing 2006
Hersteller:	Springer Berlin Springer Berlin Heidelberg Universitext
Maße:	235 x 155 x 19 mm
Von/Mit:	Vladimir I. Arnold
Erscheinungsdatum:	19.06.2006
Gewicht:	0,522 kg

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