Ebook: Analysis on Manifolds

A substantial course in real analysis is an esential 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 strightforward to the challenging . The book evolved from courses on real analysis taught by the author at the Massachusetts INstitute of Technology.