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

• Κύριος συγγραφέας: Snygg, John (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
• Θέματα: Mathematics.; Algebra.; Applied mathematics.; Engineering mathematics.; Differential geometry.; Mathematical physics.; Physics.; Differential Geometry.; Mathematical Methods in Physics.; Mathematical Physics.; Mathematics, general.; Applications of Mathematics.

Differential geometry is the study of curvature and calculus of curves and surfaces.  Because of an historical accident, the Geometric Algebra devised by William Kingdom Clifford (1845–1879) has been overlooked in favor of the more complicated and less powerful formalism of differential forms and ta...

Πίνακας περιεχομένων:

• 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.