Dynamical Systems

MATH 440 treats ODEs as geometric objects: instead of hunting for closed-form solutions, you study how trajectories organize themselves in phase space — fixed points, periodic orbits, invariant manifolds, and the bifurcations that reshape them. Expect rigorous proofs (existence-uniqueness via contraction mappings, Hartman-Grobman, Floquet, stable/unstable/center manifold theorems) carried out through three homework sets, a midterm, a project, and a final. It builds on MATH 302/ODE and real analysis, and is the natural bridge into chaos theory, ergodic theory, and the dynamical-systems flavor of applied math used in physics, biology, and control.