A New Approach to Differential Geometry using Clifford's Geometric Algebra (e-book) (used book) | bookbook.eu

Description

Differential geometry is the study of the curvature and calculus of curves and surfaces. The conceptual complications introduced by a multitude of spaces and mappings normally required in the study of differential geometry usually postpones the topic to graduate-level courses. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an undergraduate level of differential geometry by introducing Clifford algebra. This presentation is relevant since Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Key features include: a rare undergraduate-level approach to differential geometry; brief biographies of historically relevant mathematicians and physicists; significant aspects of general relativity and Riemannian geometry and chapter-by-chapter exercises. This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities. This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.