Overview: New edition extensively revised and clarified, and topics have been substantially rearranged.Introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, mu.This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, f
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