Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 423–437 | Cite as

Coordinate Free Integrals in Geometric Calculus

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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 \({\mathbb{R}}\). It may lead to both practical applications and help unveil new connections to various fields of mathematics.

Keywords

Geometric algebra Geometric Calculus Integration Coordinate freedom 

Mathematics Subject Classification

Primary 58C35 Secondary 15A66 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Science InstituteUniversity of IcelandReykjavikIceland

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