A New Approach to Differential Geometry us...

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Sprache: Englisch

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Beschreibung

Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.

Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Zusammenfassung

Includes chapter-by-chapter exercises

Provides a rare undergraduate-level approach to the subject matter

Promotes the application of Clifford algebra to differential geometry

Presents a significant portion of general relativity without reference to such Newtonian terms as "force", "momentum", or "energy"

Only up-to-date title of its kind

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- Introduction.- Clifford Algebra in Euclidean 3-Space.- Clifford Algebra in Minkowski 4-Space.- Clifford Algebra in Flat n-Space.- Curved Spaces.- The Gauss-Bonnet Formula.- Non-Euclidean (Hyperbolic) Geometry.- Some Extrinsic Geometry in E^n.- Ruled Surfaces Continued.- Lines of Curvature.- Minimal Surfaces.- Some General Relativity.- Matrix Representation of a Clifford Algebra.- Construction of Coordinate Dirac Matrices.- A Few Terms of the Taylor's Series for the Urd¿-Copernican Model for the Outer Planets.- A Few Terms of the Taylor's Series for Kepler's Orbits.- References.- Index.

Details

Erscheinungsjahr:	2011
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xvii 465 S. 102 s/w Illustr. 465 p. 102 illus.
ISBN-13:	9780817682828
ISBN-10:	0817682821
Sprache:	Englisch
Herstellernummer:	80063751
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Snygg, John
Hersteller:	Birkhuser Boston Birkhäuser Boston
Maße:	241 x 160 x 32 mm
Von/Mit:	John Snygg
Erscheinungsdatum:	08.12.2011
Gewicht:	0,887 kg

Artikel-ID: 106912117