I asked a similar question, but I realized the question is too vague and it's better to start a new one:
We know that there are two usually used formulations of Stoke's theorem. One is vector calculus's usage of Stoke's theorem called Kelvin-Stokes theorem. And one is Stoke's theorem that involves manifolds and boundary of mainfolds and differential forms.
The question is, how does one derive Kelvin-Stokes theorem from the general manifold formulation of Stoke's theorem?