Studies the qualitative geometrical theory of ordinary differential equations. Includes basic well posedness; linear systems and periodic systems; stability theory; perturbation of linear systems; center manifold theorem; periodic solutions and Poincaré-Bendixson theory; Hopf bifurcation; introduction to chaotic dynamics; control theoretic questions; differential geometric methods. Prerequisite: MATH 2310, 3250, 3351 or instructor permission.