How to apply the divergence theorem to a parametric surface

139 Views Asked by At

let $$F(r(u,v))= P(r(u,v)) i + Q(r(u,v))j + R(r(u,v))k$$ be a vector field in $R^3$ and $$ r(u,v)= x(u,v) i + y(u,v) j + z(u,v) k $$ is the equation of a closed parametric surface how do we apply the divergence theorem to the surface integral $$\iint_S F(r(u,v)). dS$$ I'm also a bit confused about how to find the divergence of the vector field in terms of the parameters