Coordinate free integrals in Geometric Calculus
arXiv:1509.08403 · doi:10.1007/s00006-016-0655-0
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.
20 pages, 1 figure. Add details on orientation of subspaces, and mention a more systematic method