Dynamical Systems

Dynamical systems is the geometric, qualitative study of ODEs and maps: instead of solving equations explicitly, you ask what trajectories look like in phase space, whether they settle, oscillate, or behave chaotically, and prove it rigorously. Expect a steady stream of problem sets working through existence and uniqueness, Hartman-Grobman, Floquet theory, invariant manifolds, and bifurcations, plus a project that pushes one topic deeper. The course assumes solid real analysis and ODE background, and it's the standard gateway into research areas like chaos, Hamiltonian mechanics, ergodic theory, and applied modeling across physics and biology.