The fundamental theorem of geometric calculus via a generalized Riemann integral

1998/07/06 by Alan Macdonald, Macdonald, Alan
Mathematics · Physics and Astronomy · #58C35 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:58C35

paper · pdf · doi:10.48550/arxiv.math/9807024

To appear in Advances in Applied Clifford Algebras

arxiv created 1998/07/06 · arxiv updated 2009/11/30

Abstract

Using recent advances in integration theory, we give a proof of the fundamental theorem of geometric calculus. We assume only that the tangential derivative ∇_VF exists and is Lebesgue integrable. We also give sufficient conditions that ∇_VF exists.

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