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Lee, John:
Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218) - gebunden oder broschiert

2012

ISBN: 1441999817

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ISBN: 9781441999818

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Details zum Buch
Introduction to Smooth Manifolds: 218 (Graduate Texts in Mathematics, 218)
Autor:
Titel:
ISBN-Nummer:

1441999817


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.

Detailangaben zum Buch - Introduction to Smooth Manifolds: 218 (Graduate Texts in Mathematics, 218)


EAN (ISBN-13): 9781441999818
ISBN (ISBN-10): 1441999817
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2012
Herausgeber: Springer
708 Seiten
Gewicht: 1,200 kg
Sprache: Englisch

Buch in der Datenbank seit 2008-01-20T10:17:42+01:00 (Berlin)
Detailseite zuletzt geändert am 2024-05-06T00:52:18+02:00 (Berlin)
ISBN/EAN: 1441999817

ISBN - alternative Schreibweisen:
1-4419-9981-7, 978-1-4419-9981-8
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: john lee, introduction smooth manifolds, frobenius
Titel des Buches: introduction manifolds, smooth manifolds, graduate text mathematics, 218, the graduate, john lee, intr, mani, smooth manifold, graduate texts mathematics

Daten vom Verlag:

Autor/in: John Lee
Titel: Graduate Texts in Mathematics; Introduction to Smooth Manifolds
Verlag: Springer; Springer US
708 Seiten
Erscheinungsjahr: 2012-08-26
New York; NY; US
Gedruckt / Hergestellt in Niederlande.
Sprache: Englisch
74,89 € (DE)
76,99 € (AT)
83,00 CHF (CH)
POD
XVI, 708 p.

BB; Hardcover, Softcover / Mathematik/Geometrie; Differentielle und Riemannsche Geometrie; Verstehen; Frobenius theorem; Lie group; Sard’s theorem; Smooth structures; Stokes's theorem; Tangent vectors and covectors; Whitney approximation theorem; Whitney embedding theorem; de Rham cohomology; differential forms; first-order partial differential equations; foliations; immersed and embedded submanifolds; smooth manifolds; tensors; vector bundles; vector fields and flows; Differential Geometry; BC

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 newtopics 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.
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, much earlier in the text Added topics include 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 Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras
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