The course gives an introduction to smooth manifolds. It covers tangent bundles, vector fields and integral curves (ordinary differential equations), Lie groups, differential forms, and integration.

Abstract: This article concerns the construction of a scalar valued analytic map, which we term as the navigation function, on three-manifold with boundary as a disjoint union of Hopf tori. Although ...

What began with a focus on weather forecasting has evolved toward addressing errors in scientific modeling. In the collaborative environment of the Penn State Institute for Computational and Data ...