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Graduate Texts in Mathematics Ser.: Introduction to Smooth Manifolds 2nd Ed
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- Buy It NowGraduate Texts in Mathematics Ser.: Introduction to Smooth Manifolds 2nd Ed
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eBay item number:187036018111
Item specifics
- Condition
- ISBN
- 9781441999818
About this product
Product Identifiers
Publisher
Springer New York
ISBN-10
1441999817
ISBN-13
9781441999818
eBay Product ID (ePID)
117315967
Product Key Features
Number of Pages
Xvi, 708 Pages
Publication Name
Introduction to Smooth Manifolds
Language
English
Publication Year
2012
Subject
Geometry / Differential
Type
Textbook
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
0.6 in
Item Weight
43.9 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
Reviews
From the reviews of the second edition: "It starts off with five chapters covering basics on smooth manifolds up to submersions, immersions, embeddings, and of course submanifolds. ... the book under review is laden with excellent exercises that significantly further the reader's understanding of the material, and Lee takes great pains to motivate everything well all the way through ... . a fine graduate-level text for differential geometers as well as people like me, fellow travelers who always wish they knew more about such a beautiful subject." (Michael Berg, MAA Reviews, October, 2012)
Dewey Edition
21
Series Volume Number
218
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
514/.3
Table Of Content
Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves and Flows.- 10 Vector Bundles.- 11 The Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem.- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22 Symplectic Manifolds.- Appendix A: Review of Topology.- Appendix B: Review of Linear Algebra.- Appendix C: Review of Calculus.- Appendix D: Review of Differential Equations.- References.- Notation Index.- Subject Index.
Synopsis
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 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 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.
LC Classification Number
QA641-670
Item description from the seller
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- s***r (50)- Feedback left by buyer.Past monthVerified purchaseThe price was perfectly reasonable for the product, and the book arrived promptly and in great condition—like new, as described: the slightest bit of noticeable use and that was it. The seller wrapped it in literally 6 layers of protection (cardboard, bubble wrap, waterproof, etc.), which seemed like overkill but was much appreciated. My wife was so impressed that she demanded I leave a positive review immediately—and she was right. I’d be happy to do business with this seller again.
- m***_ (362)- Feedback left by buyer.Past 6 monthsVerified purchaseThe seller shipped the book quickly, tracked for added security and it arrived on time. Around 3 weeks which isn't bad at all. The book was exactly as advertised by the seller. I had no problem comunicating with the seller, he answered all my questions. He also packed the book very well so it wouldn't get damaged during shipping. It arrived as good as new. I'm very satisfied, the seller showed a very customer friendly /professional attitude. Hence my 5/5 positive feedback to him.Engineering a Compiler by Linda Torczon and Keith Cooper (2011, Hardcover) (#176727972484)
- a***4 (54)- Feedback left by buyer.Past 6 monthsVerified purchasePerfect shipping. My package came through with great timing, Everything looked exactly like it did in the previous description. Also the seller did an excellent job! Using good wrapping solution to make sure nothing got damaged, and I really do enjoy my package 📦 that was sent so most definitely recommend anyone who’s looking for something classic movie wise or tv series etc. To check out what great offers you will get to receive, rest assured that you will certainly not be disappointed.
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Most relevant reviews
- 26 May, 2021
Great book.
Verified purchase: YesCondition: NewSold by: textsupply
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