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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).
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.
Inhaltsverzeichnis
Basic Concepts.- Basic Theorems.- Linear Systems.- Proofs of the Main Theorems.- Differential Equations on Manifolds.
Details
Erscheinungsjahr: | 2006 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
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-Verlag GmbH
Springer Berlin Heidelberg Universitext |
Verantwortliche Person für die EU: | Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de |
Maße: | 235 x 155 x 19 mm |
Von/Mit: | Vladimir I. Arnold |
Erscheinungsdatum: | 19.06.2006 |
Gewicht: | 0,522 kg |
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.
Inhaltsverzeichnis
Basic Concepts.- Basic Theorems.- Linear Systems.- Proofs of the Main Theorems.- Differential Equations on Manifolds.
Details
Erscheinungsjahr: | 2006 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
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-Verlag GmbH
Springer Berlin Heidelberg Universitext |
Verantwortliche Person für die EU: | Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de |
Maße: | 235 x 155 x 19 mm |
Von/Mit: | Vladimir I. Arnold |
Erscheinungsdatum: | 19.06.2006 |
Gewicht: | 0,522 kg |
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