Ohhhhh, thank you! It seems obvious now, but the order I do the cross product is just another way to manipulate the orientation of the surface.
To sum up, the order of r(R,θ) and r(θ,R) do not matter. But the cross product will give me an orientation that will point one direction and I have...
Hello everybody!
My question has to do with the parameterization of 3D surfaces from 3 variables to 2. Specifically, I'm trying to figure out an aspect of the cross product of the directional derivatives of the parameterization to solve flux integrals. Trying to convert:
∫∫SF dS = ∫∫DF(r(u,v))...