I'm back with more questions! I'm wondering what conditions must a manifold satisfy to be able to use Stokes' Theorem. I understand that it must be orientable, but does it have to necessarily be smooth? I tried to see if it was possible to prove Cauchy's Residue Theorem and Cauchy's Integral Formula using Stokes' Theorem, but I got stuck with results that don't make sense. Both require that an integrand can be meromorphic, so I'm not sure that Stokes' Theorem will necessarily apply to nonsmooth manifolds.