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 -