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008 160915s2014 gw | s |||| 0|eng d
020 _a9783319017365
_9978-3-319-01736-5
024 7 _a10.1007/978-3-319-01736-5
_2doi
035 _ato000542126
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aBorceux, Francis.
_eauthor.
_9448012
245 1 2 _aA Differential Approach to Geometry
_helectronic resource
_bGeometric Trilogy III /
_cby Francis Borceux.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXVI, 452 p. 159 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _aIntroduction -- Preface -- 1.The Genesis of Differential Methods -- 2.Plane Curves -- 3.A Museum of Curves -- 4.Skew Curves -- 5.Local Theory of Surfaces -- 6.Towards Riemannian Geometry -- 7.Elements of Global Theory of Surfaces -- Appendices: A.Topology -- B.Differential Equations -- Index -- Bibliography.
520 _aThis book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providing an integrated presentation fully accessible to undergraduate-level students.   At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions, not just those constructed from polynomials. During the 18th century, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter this fascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincaré characteristics) associated with a surface gives you a lot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry, the geometry that underlies the theory of relativity.   The book is of interest to all those who teach classical differential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to “intuitively” introduce students to the highly technical nature of this branch of mathematics, in particular when preparing students for courses on relativity.
650 0 _amathematics.
_9566183
650 0 _aGeometry.
_9303683
650 0 _aGlobal differential geometry.
_9566343
650 1 4 _aMathematics.
_9566184
650 2 4 _aGeometry.
_9303683
650 2 4 _aDifferential Geometry.
_9566344
650 2 4 _aHistory of Mathematical Sciences.
_9296777
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-01736-5
912 _aZDB-2-SMA
999 _c399995