000 02899nam a22004815i 4500
001 978-1-4614-7732-7
003 DE-He213
005 20140220082830.0
007 cr nn 008mamaa
008 130709s2013 xxu| s |||| 0|eng d
020 _a9781461477327
_9978-1-4614-7732-7
024 7 _a10.1007/978-1-4614-7732-7
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
100 1 _aMcInerney, Andrew.
_eauthor.
245 1 0 _aFirst Steps in Differential Geometry
_h[electronic resource] :
_bRiemannian, Contact, Symplectic /
_cby Andrew McInerney.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXIII, 410 p. 54 illus., 25 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUndergraduate Texts in Mathematics,
_x0172-6056
505 0 _aBasic Objects and Notation -- Linear Algebra Essentials -- Advanced Calculus -- Differential Forms and Tensors -- Riemannian Geometry -- Contact Geometry -- Symplectic Geometry -- References -- Index.
520 _aDifferential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
650 0 _aMathematics.
650 0 _aGlobal analysis.
650 0 _aGlobal differential geometry.
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461477310
830 0 _aUndergraduate Texts in Mathematics,
_x0172-6056
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-7732-7
912 _aZDB-2-SMA
999 _c95974
_d95974