Differentiable manifolds; vector bundles, existence theorem for ODE, flows, sprays; vector fields, differential operators, Lie and exterior derivatives; Poincare Lemma, Darboux's Theorem; Frobenius's Theorem, Lie groups; de Rham cohomology.
Prereq: Grad standing or all of 5201 (652), and either 2568 (568) or 572, and 2153.01 (254). Not open to students with credit for 765.