I Which Form of Maxwell's Equations is More Useful? (Integral versus Differential)

There are two forms of the Maxwell equations, one is the differential form, the other is the integral form. Which one is more useful?
 

Vanadium 50

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Depends on the problem you are trying to solve.
 

rude man

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I like the differential form because (1) they apply to every point in space, not just some volume or surface; and (2) with just two purely mathematical relations, to wit, the Stokes and divergence (aka Gauss's) theorems, all the integral relations are immediately derivable from the differential ones.
 

vanhees71

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The fundamental form of the Maxwell equations is the local, i.e., differential form. A local field theoretical description is in a sense the natural mathematical form for relativistic field theories, and Maxwell's electromagnetism is a paradigmatic example for a relativistic field theory.
 

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