Coordinate free integrals in Geometric Calculus
Differential Geometry
2016-09-15 v2 Mathematical Physics
math.MP
Rings and Algebras
Abstract
We introduce a method for evaluating integrals in geometric calculus without introducing coordinates, based on using the fundamental theorem of calculus repeatedly and cutting the resulting manifolds so as to create a boundary and allow for the existence of an antiderivative at each step. The method is a direct generalization of the usual method of integration on function of a real variable. It may lead to both practical applications and help unveil new connections to various fields of mathematics.
Keywords
Cite
@article{arxiv.1509.08403,
title = {Coordinate free integrals in Geometric Calculus},
author = {Timo Alho},
journal= {arXiv preprint arXiv:1509.08403},
year = {2016}
}
Comments
20 pages, 1 figure. Add details on orientation of subspaces, and mention a more systematic method