Abstract
We construct geometric calculus on an oriented k-surface embedded in Euclidean space by utilizing the notion of an oriented k-surface as the limit set of a sequence of k-chains. This method provides insight into the relationship between the vector derivative, and the Fundamental Theorem of Calculus and Residue Theorem. It should be of practical value in numerical finite difference calculations with integral and differential equations in Clifford algebra.
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© 1992 Springer Science+Business Media Dordrecht
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Sobczyk, G.E. (1992). Simplicial calculus with Geometric Algebra. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_29
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DOI: https://doi.org/10.1007/978-94-015-8090-8_29
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4130-2
Online ISBN: 978-94-015-8090-8
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