000			03538nam a22004935i 4500
001			978-0-8176-8283-5
003			DE-He213
005			20140220083227.0
007			cr nn 008mamaa
008			111207s2012 xxu| s |||| 0|eng d
020			_a9780817682835 _9978-0-8176-8283-5
024	7		_a10.1007/978-0-8176-8283-5 _2doi
050		4	_aQA641-670
072		7	_aPBMP _2bicssc
072		7	_aMAT012030 _2bisacsh
082	0	4	_a516.36 _223
100	1		_aSnygg, John. _eauthor.
245	1	2	_aA New Approach to Differential Geometry using Clifford's Geometric Algebra _h[electronic resource] / _cby John Snygg.
264		1	_aBoston, MA : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2012.
300			_aXVII, 465p. 102 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- Introduction -- Clifford Algebra in Euclidean 3-Space -- Clifford Algebra in Minkowski 4-Space -- Clifford Algebra in Flat n-Space -- Curved Spaces -- The Gauss-Bonnet Formula -- Non-Euclidean (Hyperbolic) Geometry -- Some Extrinsic Geometry in E^n -- Ruled Surfaces Continued -- Lines of Curvature -- Minimal Surfaces -- Some General Relativity -- Matrix Representation of a Clifford Algebra -- Construction of Coordinate Dirac Matrices -- A Few Terms of the Taylor's Series for the Urdī-Copernican Model for the Outer Planets -- A Few Terms of the Taylor's Series for Kepler's Orbits -- References -- Index.
520			_aDifferential geometry is the study of curvature and calculus of curves and surfaces.  Because of an historical accident, the Geometric Algebra devised by William Kingdom Clifford (1845–1879) has been overlooked in favor of the more complicated and less powerful formalism of differential forms and tangent vectors to deal with differential geometry.  Fortuitously a student who has completed an undergraduate course in linear algebra is better prepared to deal with the intricacies of Clifford algebra than with the formalism currently used.  Clifford algebra enables one to demonstrate a close relation between curvature and certain rotations.  This is an advantage both conceptually and computationally—particularly in higher dimensions. Key features and topics include: * a unique undergraduate-level approach to differential geometry; * brief biographies of historically relevant mathematicians and physicists; * some aspects of special and general relativity accessible to undergraduates with no knowledge of Newtonian physics; * chapter-by-chapter exercises. The textbook will also serve as a useful classroom resource primarily for undergraduates as well as beginning-level graduate students; researchers in the algebra and physics communities may also find the book useful as a self-study guide.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aGlobal differential geometry.
650		0	_aMathematical physics.
650	1	4	_aMathematics.
650	2	4	_aDifferential Geometry.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aMathematical Physics.
650	2	4	_aMathematics, general.
650	2	4	_aAlgebra.
650	2	4	_aApplications of Mathematics.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817682828
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8283-5
912			_aZDB-2-SMA
999			_c100231 _d100231