Ordinary Differential Equations - Introduction to the Theory of Ordinary Differential Equations in the Real Domain

Abstract

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. Caratheodory Theory of Differential Equations. Differential Relations. Appendices. References. Index of Symbols. Subject Index.