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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. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now 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'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, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.

This book will include line art in sepia ink for 70 off-white pages to color inspired by blocks featured in the Farmer's Wife Sampler Quilt Books. The geometric nature of patchwork quilt designs and blocks lend themselves perfectly to coloring book pages. The fabric line art has been rendered from actual vintage yardage. And, the blocks and quilt layouts could be worked up into actual quilts if you're so inclined. Tool-making or culture, language or religious belief: ever since Darwin, thinkers have struggled to identify what fundamentally differentiates human beings from other animals. In this much-anticipated book, Michael Tomasello weaves his twenty years of comparative studies of humans and great apes into a compelling argument that cooperative social interaction is the key to our cognitive uniqueness. Once our ancestors learned to put their heads together with others Introduction to Smooth Manifolds free pdf to pursue shared goals, humankind was on an evolutionary path all its own.

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Author: John M. Lee
Number of Pages: 724 pages
Published Date: 01 Oct 2012
Publisher: Springer-Verlag New York Inc.
Publication Country: New York, NY, United States
Language: English
ISBN: 9781441999818
Download Link: Click Here
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