Ordinary Differential Equations

Description

This is an elementary textbook, based closely on the lecture notes reviewed above [##13674–13676]. However, as one would expect from the author, it is a most unusual book and, though most of the standard topics are covered, a great deal of routine and computational material is omitted and there is heavy emphasis on geometric qualitative ideas, on the one hand, and on applications to mechanics (both for their own sake and for a motivating source of ideas), on the other. Although the formal prerequisites are slight, some parts of the book (such as the last chapter) do require considerable mathematical maturity.
Chapter headings: Basic concepts (including vector fields and the tangent space) (pp. 7–46); Basic theorems (including existence, continuous dependence, phase curves of autonomous systems, etc.) (pp. 47–85); Linear systems (including the topological classification of singular points and stability theory) (pp. 86–184); Proofs of the basic theorems (pp. 185–203); Differential equations on manifolds (pp. 204–233).
This book is to be most highly recommended. The translations reviewed below [##13678, 13679] should help it reach the wide audience it deserves.

Reviewed by J. Burlak

This book puts a clear emphasis on the qualitative and geometric properties of ordinary differential equations and their solutions, helping the student to get a feel for the subject. The text is rich with examples and connections with mechanics and proceeds with physical reasoning, using it as a convenient shorthand for much longer formal mathematical reasoning. 272 illustrations.

cited here

Characteristic equation 129, 134

Characteristics of an equation 136