000			03864nam a22005175i 4500
003			DE-He213
005			20191011040838.0
007			cr nn 008mamaa
008			101013s2011 xxu| s |||| 0|eng d
020	6	4	_a9781441974006 _9978-1-4419-7400-6
024	8	7	_a10.1007/978-1-4419-7400-6 _2doi
050	8	4	_aQA613-613.8
050	8	4	_aQA613.6-613.66
072	8	7	_aPBMS _2bicssc
072	8	7	_aPBPH _2bicssc
072	8	7	_aMAT038000 _2bisacsh
082			_a514.34 _223
100	8	1	_aTu, Loring W. _eauthor. _963958
245			_aAn Introduction to Manifolds _h[electronic resource] / _cby Loring W. Tu.
001			000053156
300	6	4	_aXVIII, 410 p. 124 illus., 1 illus. in color. _bonline resource.
490	8	1	_aUniversitext, _x0172-5939
505	8	0	_aPreface to the Second Edition -- Preface to the First Edition -- Chapter 1. Euclidean Spaces -- Chapter 2. Manifolds -- Chapter 3. The Tangent Space -- Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms -- Chapter 6. Integration.-Chapter 7. De Rham Theory -- Appendices -- A. Point-Set Topology -- B. The Inverse Function Theorem on R(N) and Related Results -- C. Existence of a Partition of Unity in General -- D. Linear Algebra -- E. Quaternions and the Symplectic Group -- Solutions to Selected Exercises -- Hints and Solutions to Selected End-of-Section Problems -- List of Symbols -- References -- Index.
520	6	4	_aManifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology."
650	8	0	_aMathematics. _98571
650	8	0	_aGlobal analysis. _917903
650	8	0	_aGlobal differential geometry. _99530
650	8	0	_aCell aggregation _xMathematics. _912625
650			_aMathematics. _98571
650			_aManifolds and Cell Complexes (incl. Diff.Topology). _912627
650			_aGlobal Analysis and Analysis on Manifolds. _917904
650			_aDifferential Geometry. _99532
710	8	2	_aSpringerLink (Online service) _963959
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9781441973993
830	8	0	_aUniversitext, _x0172-5939 _99677
856			_uhttp://dx.doi.org/10.1007/978-1-4419-7400-6 _zde clik aquí para ver el libro electrónico
264	8	1	_aNew York, NY : _bSpringer New York, _c2011.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
999			_c52886 _d52886
942			_c05