In the typical calculus sequence, students learn a bunch of integration theorem including the Fundamental Theorem of Calculus, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. At first glance, it is not immediately clear that these theorems are related. But it turns out that they are all secretly special cases of the exact same theorem: The Generalized Stokes Theorem.
In this talk, we spend an hour exploring the connections between these theorems and how they are really the same theorem. Along the way, we introduce the concept of differential forms in a manner appropriate for a multivariable calculus student.
