Actually the former - while part of Vector Calculaus - Green;'s Theorem is often taught under the purview of Integral/Differential solutions for applied engineering problems (I am an EEE undergrad). Hence you have Stoke's Theorem, Green's function, Cauchy-Riemann equations all in one big tome. We also did Vector Calculus where we revisited the same notions in a different way from first principles.
And yes, Layperson is also right. It has been over a layperson year since I last looked at them.