{"product_id":"introduction-to-smooth-manifolds-9781441999818","title":"Introduction to Smooth Manifolds","description":"\u003cp\u003eThis 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 fewnew topics have been added  notably Sards 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.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45665887584309,"sku":"ByrdShop_1441999817","price":109.74,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9781441999818.jpg?v=1782412795","url":"https:\/\/atxbooks.com\/products\/introduction-to-smooth-manifolds-9781441999818","provider":"ATX Books","version":"1.0","type":"link"}