Ordinary Differential Equations

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.

Spis treści:
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.