Lecture, three hours; discussion, one hour. Smooth manifolds and smooth maps; inverse and implicit function theorems, submersions, immersions, submanifolds; tangent and cotangent bundles, vector bundles; differential forms, exterior differentiation, and Lie derivatives; integration, Stokes' theorem, de Rham cohomology, and computations using the Mayer-Vietoris sequences; vector fields, integral curves, distributions, Frobenius' theorem. S/U or letter grading.