Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of
Prefaces. Introduction. Existence Theorems. Linear Systems. Autonomous Systems. Stability. The Lyapunov Second Method. Periodic Solutions. Perturbation Theory: The Poincare Method. Perturbation Theory: Autonomous Systems and Bifurcation Problems. Using the Averaging Method: An Introduction. Appendix. References. Index.