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120824s2012 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781441999825 |
|
978-1-4419-9982-5 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA641-670 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
516.36 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
New York, NY : |
| -- |
Springer New York : |
| -- |
Imprint: Springer, |
| -- |
2012. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Lee, John M. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Introduction to Smooth Manifolds |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by John M. Lee. |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
2nd ed. 2012. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XV, 708 p. 150 illus. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Graduate Texts in Mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume number/sequential designation |
218 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Global differential geometry. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Differential Geometry. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9781441999818 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-1-4419-9982-5 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
