## The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

Publication: Research - peer-review › Report – Annual report year: 2006

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**The direct Flow parametric Proof of Gauss' Divergence Theorem revisited.** / Markvorsen, Steen.

Publication: Research - peer-review › Report – Annual report year: 2006

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*The direct Flow parametric Proof of Gauss' Divergence Theorem revisited*. Department of Mathematics, Technical University of Denmark. Mat-Report, no. 2006-15

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*The direct Flow parametric Proof of Gauss' Divergence Theorem revisited*. Department of Mathematics, Technical University of Denmark. (Mat-Report; No. 2006-15).

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*The direct Flow parametric Proof of Gauss' Divergence Theorem revisited*Department of Mathematics, Technical University of Denmark. 2006. (Mat-Report; Journal number 2006-15).

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### RIS

TY - RPRT

T1 - The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

AU - Markvorsen,Steen

PY - 2006

Y1 - 2006

N2 - The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuition further by unfolding and visualizing a few examples with increasing complexity. In these examples we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem.

AB - The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuition further by unfolding and visualizing a few examples with increasing complexity. In these examples we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem.

KW - Curriculum, visualization, and process oriented learning

KW - Vector fields and integral curves

KW - Gauss' divergence theorem in 3D

M3 - Report

BT - The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

PB - Department of Mathematics, Technical University of Denmark

ER -