Stoke's theorem.

For our surfaces, we will use parametrizations (v.s. section 2).

Let be a surface whose boundary is the curve in space; we denote a unit vector, normal to the surface .

Then:

Denote the interior of the ellipse . We have:

- The curl:

- The projection of
onto the
*xy*-plane is the unit disk ; a unit vector, normal to is . - .
- According to Stoke's theorem: