I've been reading the text: Electricity and Magnetism, by Purcell. I understand about the integral forms describing the electric field, but when trying to answer questions at the end of the chapter on Gauss's and Stokes's therorems I have not been able two. These two theorems supposedly transform the integral equations that describe an electric field into differential equations, yet there are still integrals in the equations: Gauss: [tex]Integrate[F*da,over surface]=Integrate[div F*dv,over volume][/tex] [tex]div F=4\pi\rho, del^2*potential=-4\pi\rho[/tex] Stokes: [tex]Integrate[F*ds,over circ.]=Integrate[curl F*da,over surface][/tex] [tex]del X A[/tex] Questions: 1. I'm having trouble with looking at field lines and judging if div F=0 (or not zero) or curl F=0 (or not zero) 2. How to calculate flux/volume for Gauss problems. I see in the book they use the midpoint. Or flux/area for Stokes problems. Why do the choose the midpoint? 3. Also would someone explain the sidways derivative of the curl, I don't understand why it is the way it is.