عنوان

Introduction to smooth manifolds /

شابک

1441999817

شابک

1441999825

شابک

1489994750

شابک

9781441999818

شابک

9781441999825

شابک

9781489994752

کد کشور

bnb

شماره

b623607

عنوان اصلي

Introduction to smooth manifolds /

نام عام مواد

[Book]

نام نخستين پديدآور

John M. Lee.

وضعيت ويراست

2nd ed.

محل نشرو پخش و غیره

London :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2013.

نام خاص و کميت اثر

xv, 708 pages :

ساير جزييات

illustrations ;

ابعاد

24 cm

عنوان فروست

Graduate texts in mathematics ;

مشخصه جلد

218

متن يادداشت

Includes bibliographical references (pages 675-677) and indexes.

متن يادداشت

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 contangent 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 -- Appendices.

بدون عنوان

0

متن يادداشت

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.

عنوان

Introduction to smooth manifolds.

شماره استاندارد بين المللي کتاب و موسيقي

9781441999818

موضوع مستند نشده

Manifolds (Mathematics)

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Manifolds (Mathematics)

موضوع مستند نشده

QA

شماره

ويراست

شماره رده

نشانه اثر

شماره رده

مستند نام اشخاص تاييد نشده

Lee, John M.,1950-

تاريخ عمليات

20200617082716.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y