000			03442nam a22004455i 4500
001			978-3-319-01736-5
003			DE-He213
005			20140220082509.0
007			cr nn 008mamaa
008			131108s2014 gw | s |||| 0|eng d
020			_a9783319017365 _9978-3-319-01736-5
024	7		_a10.1007/978-3-319-01736-5 _2doi
050		4	_aQA440-699
072		7	_aPBM _2bicssc
072		7	_aMAT012000 _2bisacsh
082	0	4	_a516 _223
100	1		_aBorceux, Francis. _eauthor.
245	1	2	_aA Differential Approach to Geometry _h[electronic resource] : _bGeometric Trilogy III / _cby Francis Borceux.
264		1	_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
347			_atext file _bPDF _2rda
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.
650		0	_aGeometry.
650		0	_aGlobal differential geometry.
650	1	4	_aMathematics.
650	2	4	_aGeometry.
650	2	4	_aDifferential Geometry.
650	2	4	_aHistory of Mathematical Sciences.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319017358
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-319-01736-5
912			_aZDB-2-SMA
999			_c92726 _d92726