Prerequisite concepts
The curl of the magnetic vector potential is the magnetic field
The negative gradient of the electric potential is the electric field
The divergence of the electric field is equal to $\rho / \epsilon_0$
The divergence of the magnetic field is zero
The curl of the electric field is zero in electrostatics
The divergence of the curl is equal to $\mu_0$ times the current (in magneto-statics)
Maxwell's Equations
FIXME
The curl of the electric field is zero in electrostatics
FIXME: Long description + Does this really need the pre-req of the derivative of a constant is zero. What is the thing that is constant if the curl is zero?