Pressley Elementary Differential Geometry

2. Auflage 2010
ISBN: 978-1-84882-891-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 395 Seiten, eBook

Reihe: Springer Undergraduate Mathematics Series

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.comul

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Pressley, A.N.

Inhaltsverzeichnis

Curves in the plane and in space.- How much does a curve curve?.- Global properties of curves.- Surfaces in three dimensions.- Examples of surfaces.- The first fundamental form.- Curvature of surfaces.- Gaussian, mean and principal curvatures.- Geodesics.- Gauss’ Theorema Egregium.- Hyperbolic geometry.- Minimal surfaces.- The Gauss–Bonnet theorem.

Über Autor(innen)

Andrew Pressley is Professor of Mathematics at King’s College London, UK.