Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold

Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface th

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differen

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced