>>16707389
>but the integral form is better behaved mathematically when dealing with physical point charges
I would argue the opposite is true. Point charges in the differential form require Dirac deltas. So you need the notion of a Dirac distribution or a Dirac measure blah blah blah. The integral form doesn't care; you just have a bunch of charge in the interior of a manifold and and when you integrate it out, you just get a number, the total charge inside.

The differential form is "more fundamental" in the sense that the differential form is the equations of motion of the Maxwell action, which can be represented entirely via differential forms:
[eqn]S_{\mathrm{Maxwell}}=\int_M \left(F\wedge\star{F} - A\wedge\star{J}\right)[/eqn]
where A is a one-form (the EM potential), d is the exterior derivative, F = dA (the Faraday tensor), and you have all the usual wedge product and Hodge star business.

The integral form cannot be derived this way. You need to start with the differential equations, then use Stokes' theorem on it. So it's extra steps that require differential equations a priori and in this sense it's "less fundamental".

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How come Maxwell's equations have 2 different forms? Which one is real?E=mc2 doesn't have 2 forms, why the difference?

How come Maxwell's equations have 2 different forms? Which one is real?
E=mc2 doesn't have 2 forms, why the difference?