Geometry from a Differentiable Viewpoint (eBook)
Cambridge University Press (Verlag)
978-1-139-79301-8 (ISBN)
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.
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.
| Erscheint lt. Verlag | 22.10.2012 |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Technik | |
| ISBN-10 | 1-139-79301-2 / 1139793012 |
| ISBN-13 | 978-1-139-79301-8 / 9781139793018 |
| Haben Sie eine Frage zum Produkt? |
EPUB (Adobe DRM)Kopierschutz: Adobe-DRM
Adobe-DRM ist ein Kopierschutz, der das eBook vor Mißbrauch schützen soll. Dabei wird das eBook bereits beim Download auf Ihre persönliche Adobe-ID autorisiert. Lesen können Sie das eBook dann nur auf den Geräten, welche ebenfalls auf Ihre Adobe-ID registriert sind.
Details zum Adobe-DRM
Dateiformat: EPUB (Electronic Publication)
EPUB ist ein offener Standard für eBooks und eignet sich besonders zur Darstellung von Belletristik und Sachbüchern. Der Fließtext wird dynamisch an die Display- und Schriftgröße angepasst. Auch für mobile Lesegeräte ist EPUB daher gut geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen eine
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen eine
Geräteliste und zusätzliche Hinweise
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich
