Analysis on Manifolds

After one is comfortable with analysis on Euclidean space, the next step is to study analysis on spaces that only locally look like Euclidean space. This leads us to the concept of a manifold. After some definitions, we generalize the notions of vectors and forms from Chapter 1 to the manifold setting. Integration of forms on orientable manifolds is discussed and the chapter ends with the proofs of Stokes' theorem and some of its corollaries.