/sci/ - Science & Math

Can someone explain in layman terms the generalized stokes theorem, the notation and the intuition on why it works?

I learnt green's theorem and kelvin-stokes theorem on calc 3, then I heard about generalized stokes, from which we can derive a plethora of theorems.

If you're using notation not used up to calc 3, state it beforehand. I just learned that <span class="math">\partial x[/spoiler] can denote a boundary instead of a partial operator and I guess there are more of these weird notations.

>>5806190
It's all Stokes' thrm.

Just remember that the Integral of a differentiable form ω over a boundary (surface) is equal to the derivative (curl, divergence, gradient) of that vector field over the manifold (area, volume)

I thought I was going to fail calc III until my prof on the last day presented Stokes' Thrm and tied all that bullshit together