How do we apply Stoke's Theorem?

So we learned the last theorem ever in this course today-- Stokes' Theorem. Just as magnificent as Mr. Honner made the theorem sound, it is actually pretty amazing. It basically incorporates both the Divergence Theorem and Green's Theorem into one. It states:

Let S be a smooth surface that is bounded by a simple closed curve. Then the closed integral of F dot dr is equal to the double integral of curl F dot dS, over the surface S.

In the Divergence Theorem, surface integrals and triple integrals are shown to be interrelated and it shows the flux. Green's Theorem relates line integrals (work) and double integrals. But in this theorem, it links the two theorems--surface integrals and line integrals, which makes it pretty cool.

Well, that was the last theorem you'll ever learn in this course. Make use of it on the final on Friday!

The homework for tonight was the same as yesterdays: P. 1130 # 2, 5, 8, 10, 25, 26.