> Maxwell's equations are difficult to view as a whole since they are 6 or 7 separate things that should each be understood individually
How so? You can't understand electricity and magnetism separately because they both affect each other; the clearest triumph of Maxwell's equations is that they describe electromagnetic waves, but you need the complete system of equations to do that.
I guess this description is subjective in terms of wholes or parts, but to me the each of the equations in isolation makes sense too. They all handle separate parts of electricity and of magnetism. For me, personally, I find it difficult to visualise them all at the same time. I have to look at each one carefully and then relate that to the whole which would be what we now call electromagnetism.
How so? You can't understand electricity and magnetism separately because they both affect each other; the clearest triumph of Maxwell's equations is that they describe electromagnetic waves, but you need the complete system of equations to do that.