This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students

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

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

This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and e

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