Introductory Math Seminar: Some Thoughts on Teaching: Why Physics Matters for the Integral Theorems of Vector Calculus

Vector calculus came into being in the 19th century alongside fundamental developments in physics, especially electromagnetism. It is in the context of electromagnetism that the integral theorems, in particular, find their clearest meaning and purpose. Trying to remove physics talk from pedagogy in vector calculus might seem like a good way to reduce the cognitive load on students, but, in this talk, I will argue that this approach ends up being counterproductive. I will instead argue that instruction on the integral theorems of vector calculus should involve concepts from electromagnetism at every step.