Table of contents:
Existence Theorems * Linear Systems * Autonomous Systems * Stability * The Lyapunov Second Method * Periodic Solutions * Bifurcation and Branching of Periodic Solutions * Appendix: Ascoli's Theorem; Principle of Contraction Mappings; Topological Degree.
This text, now in its second edition, presents the basic theory of ordinary differential equations and relates the topological theory used in differential equations to advanced applications in chemistry and biology. It provides new motivations for studying extension theorems and existence theorems, supplies real-world examples, gives an early introduction to the use of geometric methods and offers a novel treatment of the Sturm-Liouville theory.
Existence Theorems * Linear Systems * Autonomous Systems * Stability * The Lyapunov Second Method * Periodic Solutions * Bifurcation and Branching of Periodic Solutions * Appendix: Ascoli's Theorem; Principle of Contraction Mappings; Topological Degree.
This text, now in its second edition, presents the basic theory of ordinary differential equations and relates the topological theory used in differential equations to advanced applications in chemistry and biology. It provides new motivations for studying extension theorems and existence theorems, supplies real-world examples, gives an early introduction to the use of geometric methods and offers a novel treatment of the Sturm-Liouville theory.