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

T3 - Mat-Report

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

PB - Department of Mathematics, Technical University of Denmark

ER -