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Introduction to Smooth Manifolds,9781441999818
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Introduction to Smooth Manifolds

by
Edition:
2nd
ISBN13:

9781441999818

ISBN10:
1441999817
Format:
Hardcover
Pub. Date:
10/1/2012
Publisher(s):
Springer Verlag
List Price: $99.00
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Summary

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, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more.This second edition has been extensively revised and clarified.#xC2;#xA0;The topics have been substantially rearranged.#xC2;#xA0;The book now#xC2;#xA0;introduces the two most important analytic tools (the rank theorem and the fundamental theorem on flows) much earlier, so that they can be used throughout the book. A few new topics have been added, notably Sard#xE2;#xAC;"s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, and a brief treatment of degree theory for smooth maps between compact manifolds.The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.


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