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arXiv · 1509.08403

Coordinate free integrals in Geometric Calculus

Timo Alho
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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.

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Timo Alho. 2015-09-28. Coordinate free integrals in Geometric Calculus. https://doi.org/10.1007/s00006-016-0655-0

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