Vector Calculus Reimagined

Pretty much every calculus book states the definitions of divergence and curl with no motivation, providing a hand-wavy notion of their geometric meaning or postponing these concepts entirely until after covering the theorems of Green, Gauss and Stokes (all of which are stated out of the blue with no inkling as to why they might be true). In this talk we will derive the formulas for divergence and curl using geometric notions of flux and circulation in a way that leads naturally to those “Big Three” theorems — and provide additional suggestions for revamping the way we teach vector calculus.

• Beamer slides