000			02973cam a22003374a 4500
001			17271812
003			0
005			20151109040305.0
008			120425s2013 enkab b 001 0 eng
010			_a 2012017159
020			_a9780521116077 (hardback)
020			_a9780521133111 (pbk.)
040			_aDLC _cDLC _dDLC
042			_apcc
050	0	0	_aQA641 _b.M38 2013
082	0	0	_a516.36 _223 _bMCC/G
084			_aMAT038000 _2bisacsh
100	1		_aMcCleary, John, _d1952-
245	1	0	_aGeometry from a differentiable viewpoint / _cJohn McCleary.
250			_a2nd ed.
260			_aCambridge [England] ; _aNew York : _bCambridge University Press, _c2013.
300			_axv, 357 p. : _bill., maps ; _c27 cm.
504			_aIncludes bibliographical references (p. 341-349) and indexes.
505	8		_aMachine generated contents note: Part I. Prelude and Themes: Synthetic Methods and Results: 1. Spherical geometry; 2. Euclid; 3. The theory of parallels; 4. Non-Euclidean geometry; Part II. Development: Differential Geometry: 5. Curves in the plane; 6. Curves in space; 7. Surfaces; 8. Curvature for surfaces; 9. Metric equivalence of surfaces; 10. Geodesics; 11. The Gauss-Bonnet Theorem; 12. Constant-curvature surfaces; Part III. Recapitulation and Coda: 13. Abstract surfaces; 14. Modeling the non-Euclidean plane; 15. Epilogue: where from here?.
520			_a"The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss, and Riemann is a story that is often broken into parts - axiomatic geometry, non-Euclidean geometry, and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to differential geometry, the parts are united with all of their interrelations, motivated by the history of the parallel postulate. Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. The presentation is enlivened by historical diversions such as Hugyens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. New topics include Clairaut's relation for geodesics, Euclid's geometry of space, further properties of cycloids and map projections, and the use of transformations such as the reflections of the Beltrami disk"-- _cProvided by publisher.
650		0	_aGeometry, Differential.
650		7	_aMATHEMATICS / Topology. _2bisacsh
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cTB
999			_c263 _d263