Ordinary Differential Equations

2. Auflage 1987
ISBN: 978-0-89871-510-1
Verlag: Society for Industrial and Applied Mathematics

Buch, Englisch, Band 38, 632 Seiten, Format (B × H): 152 mm x 228 mm, Gewicht: 858 g

Reihe: Classics in Applied Mathematics

Ordinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustrates techniques involving simple topological arguments, fixed point theorems, and basic facts of functional analysis. Unlike many texts, which supply only the standard simplified theorems, Ordinary Differential Equations presents the basic theory of ODEs in a general way, making it a valuable reference. This SIAM reissue of the 1982 second edition covers invariant manifolds, perturbations, and dichotomies, making the text relevant to current studies of geometrical theory of differential equations and dynamical systems.

Autoren/Hrsg.

Hartman, Philip

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Foreword to the Classics Edition; Preface to the First Edition; Preface to the Second Edition; Errata; I: Preliminaries; II: Existence; III: Differential In qualities and Uniqueness; IV: Linear Differential Equations; V: Dependence on Initial Conditions and Parameters; VI: Total and Partial Differential Equations; VII: The Poincaré-Bendixson Theory; VIII: Plane Stationary Points; IX: Invariant Manifolds and Linearizations; X: Perturbed Linear Systems; XI: Linear Second Order Equations; XII: Use of Implicity Function and Fixed Point Theorems; XIII: Dichotomies for Solutions of Linear Equations; XIV: Miscellany on Monotomy; Hints for Exercises; References; Index.