Stokes' theorem.
type: Item
instance of: scholarly article
title: Stokes' theorem.
zbMATH Open document ID: 1059.26008
published in: Real Analysis Exchange
publication date: 2004-08-06T00:00:00Z
review text: In a nice and elementary way the Stokes theorem on the cube \([0,1]^n\) is proved using the Henstock-Kurzweil integral based on regular (cube) partitions of \([0,1]^n\) which is known to integrate every derivative in the case of \(n=1\). The main advantage of the generalized gauge integral is demonstrated in the paper without going into technical details of complicated nature. The idea is close to the heuristic approach to the Stokes theorem used by physicists and the author's approach is fully satisfactory from the rigorous viewpoint of mathematics in the simple case of the cube \([0,1]^n\). The paper is closed by showing that the integral definition of the differential of a given form (with differentiable coefficients) coincides with its ``derivative'' definition.
reviewed by: Štefan Schwabik
Mathematics Subject Classification ID: 26B20
Mathematics Subject Classification ID: 28A99
Mathematics Subject Classification ID: 58C35
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 2084007
zbMATH Keywords: Stokes theorem
zbMATH Keywords: Henstock-Kurzweil integral
zbMATH Keywords: gauge integral
author: Alan L. Macdonald
MaRDI profile type: Publication
OpenAlex ID: W4214722440
DOI: 10.14321/REALANALEXCH.27.2.0739
description: scientific article; zbMATH DE number 2084007