03531nam a22004815i 4500 978-0-8176-8283-5 DE-He213 20260521092034.0 cr nn 008mamaa 111207s2012 xxu| s |||| 0|eng d 9780817682835 99780817682835 10.1007/978-0-8176-8283-5 doi 516.36 23 Snygg, John. author. A New Approach to Differential Geometry using Clifford's Geometric Algebra [electronic resource] / by John Snygg. Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012. XVII, 465p. 102 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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 tangent vectors to deal with differential geometry.  Fortuitously a student who has completed an undergraduate course in linear algebra is better prepared to deal with the intricacies of Clifford algebra than with the formalism currently used.  Clifford algebra enables one to demonstrate a close relation between curvature and certain rotations.  This is an advantage both conceptually and computationally-particularly in higher dimensions. Key features and topics include: * a unique undergraduate-level approach to differential geometry; * brief biographies of historically relevant mathematicians and physicists; * some aspects of special and general relativity accessible to undergraduates with no knowledge of Newtonian physics; * chapter-by-chapter exercises. The textbook will also serve as a useful classroom resource primarily for undergraduates as well as beginning-level graduate students; researchers in the algebra and physics communities may also find the book useful as a self-study guide. MATHEMATICS. ALGEBRA. GLOBAL DIFFERENTIAL GEOMETRY. MATHEMATICAL PHYSICS. MATHEMATICS. DIFFERENTIAL GEOMETRY. MATHEMATICAL METHODS IN PHYSICS. MATHEMATICAL PHYSICS. MATHEMATICS, GENERAL. ALGEBRA. APPLICATIONS OF MATHEMATICS. SpringerLink (Online service) Springer eBooks Printed edition: 9780817682828 http://dx.doi.org/10.1007/978-0-8176-8283-5 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35805 35805 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 516.36 2025-10-06 08:44:40 2025-10-06 ER