A New Approach to Differential Geometry using Clifford's Geometric Algebra

(Autor)

Buch | Hardcover
465 Seiten
2011
Birkhauser Boston Inc (Verlag)
978-0-8176-8282-8 (ISBN)

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A New Approach to Differential Geometry using Clifford's Geometric Algebra - John Snygg
96,29 inkl. MwSt
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.

 

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 Urdī-Copernican Model for the Outer Planets.- A Few Terms of the Taylor's Series for Kepler's Orbits.- References.- Index.

Erscheint lt. Verlag 8.12.2011
Zusatzinfo 102 Illustrations, black and white; XVII, 465 p. 102 illus.
Verlagsort Secaucus
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
Naturwissenschaften Physik / Astronomie
Schlagworte Clifford Algebra • curved spaces • Differential Geometry • Gauss-Bonnet formula • General relativity • Non-Euclidean geometry • Taylor's series
ISBN-10 0-8176-8282-1 / 0817682821
ISBN-13 978-0-8176-8282-8 / 9780817682828
Zustand Neuware
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