Question

On the topic of line integrals, specifically Green's theorem...
I'm having trouble with this:

"Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region enclosed by the curve. If P and Q have continuous first order partial derivatives on D then
http://tutorial.math.lamar.edu/Classes/CalcIII/GreensTheorem_files/eq0001M.gif"

My question is, what does " If P and Q have continuous first order partial derivatives on D" mean exactly? anybody know?

Answer 1

Green theorem is just special case of Stokes theorem in the plane.
If those two terms are equal then it means there is no curl on the field on that plane.