in a general frame (say the lab) are given by
where the 
matrices take you from the MCRF to the lab frame.
The rest of the problem is just filling in the algebra in section 4.1 of the lecture notes.
. We can therefore write the four- force as
Substituting for 
from Maxwell's equations gives
The problem now is to manipulate the above into the required form. Remember a bottle of wine rests on this one!!