#MTBoS: There is a beautiful way to teach the fundamental theorems of vector #calculus! In this thread, I'll outline a natural, intuitive approach. References at the end. Thanks to @Quasilocal for starting this conversation.
1. In single variable calculus, we define the derivatives as an instantaneous rate of change, via a limit. We can define curl and div analogously as measures of rotation (circulation density) and expansion (flux density).
@HigherMathNotes @Quasilocal I think of the Fundamental Theorem of Line Integrals as conservation of total energy, and the Divergence Theorem as conservation of mass. By process of elimination, Stokes should be conservation of angular momentum. But I’m not sure how to make that argument.
@HigherMathNotes @Quasilocal The physics potato 🥔