000			02147pam a2200253 i 4500
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005			20250102224545.0
008			081109s1979 nyua |b 001 0 eng d
020			_a0387903577
039		9	_a202301160947 _bshakra _c201402040055 _dVLOAD _c201007211309 _dmalmash _c200811101456 _dvenkatrajand _y200811091245 _zNoora
050	0	0	_aQA641 _b.T36
100	1		_aThorpe, John A. _943673
245	1	0	_aElementary Topics in Differential Geometry / _cJohn A. Thorpe.
260			_aNew York : _bSpringer-Verlag, _cc1979.
300			_axiii, 253 p. : _bill. ; _c24 cm.
490	0		_aUndergraduate texts in mathematics
500			_aIncludes indexes.
504			_aBibliography: p. 245.
505			_aContents: Graphs and Level Sets.- Vector Fields.- The Tangent Space.- Surfaces.- Vector Fields on Surfaces; Orientation.- The Gauss Map.- Geodesics.- Parallel Transport.- The Weingarten Map.- Curvature of Plane Curves.- Arc Length and Line Integrals.- Curvature of Surfaces.- Convex Surfaces.- Parametrized Surfaces.- Local Equivalence of Surfaces and Parametrized Surfaces.- Focal Points.- Surface Area and Volume.- Minimal Surfaces.- The Exponential Map.- Surfaces with Boundary.- The Gauss-Bonnet Theorem.- Rigid Motions and Congruence.- Isometries.- Riemannian Metrics.
520			_aThis introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early without the need for preliminary chapters developing sophisticated machinery. the calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential forms are introduced only as needed for use in integration. The text, which draws significantly on students' prior knowledge of linear algebra, multivariate calculus, and differential equations, is designed for a one-semester course at the junior/senior level.
650		0	_aGeometry, Differential. _9904
942			_2lcc _n0 _cBK
999			_c20028 _d20028