Ordinary Differential Equations: Introduction and Qualitative Theory
Author: Jane Cronin
Publisher: Chapman & Hall/CRC
Intended to serve as a demanding course in ordinary differential equations, Cronin's text covers key material including the existence and properties of solutions, linear equations, autonomous equations and stability, along with more advanced topics in the periodic solutions of non-linear equations.
Who is it for? The advanced undergraduate student studying ordinary differential equations who wishes for more sophistication or rigour.
Presentation: The text is clearly laid out in a "definition-lemma-theorem-proof" rigorous style.
Would you recommend it? This is not a text for a first-year undergraduate course on differential equations in the UK. The initial chapters on existence theorems would be too hard and too abstract, which is a pity since the later chapters could be accessible. It is more suitable as a second/third-year text for a dynamical systems course, or as a graduate-level introduction to a more rigorous approach to ordinary differential equations.