Analysis on Manifolds

the long version

A substantial course in real analysis is an essential part of the preparation of any potential mathematician. Analysis on Manifolds is a thorough, class-tested approach that begins with the derivative and the Riemann integral for functions of several variables, followed by a treatment of differential forms and a proof of Stokes' theorem for manifolds in euclidean space. The book includes careful treatment of both the inverse function theorem and the change of variables theorem for n-dimensional integrals, as well as a proof of the Poincare lemma. Intended for students at the senior or first-year graduate level, this text includes more than 120 illustrations and exercises that range from the straightforward to the challenging . The book evolved from courses on real analysis taught by the author at the Massachusetts Institute of Technology. --back cover