Geometry from a Differentiable Viewpoint

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Studiebog
Geometry from a Differentiable Viewpoint
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Format:
Bog, hardback
Udgivelsesdato:
01-12-2012
Sprog:
Engelsk
Udgave:
2nd Revised edition.
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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 Huygens'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 and the use of transformations such as the reflections of the Beltrami disk.

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Udgivelsesdato:
01-12-2012
ISBN13:
9780521116077
Vægt:
800 g
Dybde:
22 mm
Bredde:
184 mm
Højde:
260 mm
Format:
Hardback
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