From Vector Analysis to Differential Forms

zbMATH Open1166.51008arXiv0811.2660MaRDI QIDQ3634343

Publication date: 25 June 2009

Abstract: In our previous paper [International Journal of Theoretical Physics, 41 (2002), 1165-1190] we have shown, following the tradition of synthetic differential geometry, that div and rot are uniquely determined, so long as we require that the divergence theorem and the Stokes theorem should hold on the infinitesimal level. In this paper we will simplify the discussion considerably in terms of differential forms, leading to the natural derivation of exterior differentiation in the usual form.

Full work available at URL: https://arxiv.org/abs/0811.2660

zbMATH Keywords

Stokes' theorem vector analysis synthetic differential geometry differential form divergence theorem exterior differentiation nilpotent infinitesimal

Mathematics Subject Classification ID

Synthetic differential geometry (51K10)

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