S413-S414 Honors Course in Analysis I-II (3-3 cr.) P: S312 or consent of instructor. Differentiable transformations defined on Euclidean space, inverse and implicit function theorems. Lebesgue integration over Euclidean space and transformation of integrals. Exterior algebra, measure and integration on manifolds. Stokes's theorem. Closed and exact forms. S413, I Sem.; S414, II Sem.