225B. Differential Geometry. Lecture, three hours; discussion, one hour. Lie derivatives, integrable distributions and Frobenius theorem, differential forms, integration and Stokes theorem, de Rham cohomology, including Mayer-Vietoris sequence, Poincare duality, Thom classes, degree theory and Euler characteristic revisited from viewpoint of de Rham cohomology, Riemannian metrics, gradients, volume forms, and interpreation of classical integral theorems as aspects of Stokes theorem for differential forms. S/U or letter grading.