Differential forms are a powerful computational and theoretical tool. They play a central role in mathematics, in such areas as analysis on manifolds and differential geometry, and in physics as well, in such areas as electromagnetism and general relativity. In this book, we present a concrete and careful introduction to differential forms, at the upper-undergraduate or beginning graduate level, designed with the needs of both mathematicians and physicists (and other users of the theory) in mind.
On the one hand, our treatment is concrete. By that we mean that we present quite a bit of material on how to do computations with differential forms, so that the reader may effectively use them.
On the other hand, our treatment is careful. ...