Advances in Applied Clifford Algebras

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

Coordinate Free Integrals in Geometric Calculus



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.


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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