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.
Curriculum, visualization, and process oriented learning; Vector fields and integral curves; Gauss' divergence theorem in 3D
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Department of Mathematics, Technical University of Denmark, 2006