Ordinary Differential Equations, Volume 13

Preliminaries. 1. Introduction. 2. On Elementary Methods of Integration. 3. Systems of Differential Equations, Vector Notation. 4. Linear Differential Equations. 5. Autonomous Linear Differential Equations. 6. Periodic Linear Differential Equations. 7. Second Order Linear Differential Equations. 8. Asymptotic Behaviour of Solutions of Linear Differential Equations. 9. Linear Boundary Value Problems. 10. Local Existence of Solutions of Nonlinear Differential Equations. Kneser Theorem. Fukuhara Theorem. 11. Uniqueness. 12. Global Properties of Solutions of Differential Equations. 13. Differentiability of the Solution with Respect to Initial Conditions. 14. Dependence of the Solution on a Parameter. 15. Exponential Stability. Hyperbolic Point, Unstable and Stable Manifold. 16. First Integrals. Partial Differential Equations. 17. Autonomous Systems of Two Differential Equations. 18. Carathéodory Theory of Differential Equations. Differential Relations. Appendices. References. Index of Symbols. Subject Index.

The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations.

The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.