I just found your channel (your videos seems to be very helpful), and my first thought was that are you really mirror writing all that? Because that is very cool actually :D
Where you've written ∇*A = 1/r^2 etc., should that be ∇^2*A? The expression on the right looks like the Laplacian, which the video says is ∇^2 (I'm just learning this stuff for the first time, so please feel free to correct me).