A rigorous treatment of the qualitative theory of ordinary differential equations and an introduction to the modern theory of dynamical systems, existence, uniqueness, and continuity theorems. Definition and properties of dynamical systems. Linearization and local behaviour of nonlinear systems. Stable Manifold theorem. Liapunov stability. Limit cycles and Poincaré-Bendixson Theorem. Introduction to bifurcations and chaotic dynamics. (Offered in even-numbered years.)
