# Electromagnetism for Mathematician

I am trying to find a book on electromagnetism for mathematician (so it has to be rigorous). Preferably a book that extensively uses Stoke's theorem for Maxwell's equations (unlike other books that on point source charge, they take Stoke's theorem on $B-\{0\}$ with $B$ being closed ball of radius 1, but this does not work, as Stoke's theorem only works for things in compact support) Preferably if it mentiones dirac delta function, hopefully it explains it as a distribution (or a measure...)

P.S. This question is posted because there is no questions about electromagnetism books for mathematician. I have background in mathematics as John Lee Smooth Manifolds.

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In addition, I have seen in Special Relativity have a 2-form called action and saw that electric field and magnetic field can be read from by looking at specific coefficients of its components. However, I do not understand how and why you can read these fields from that in that specific coordinates. To specify, I meant from here: math.toronto.edu/~drorbn/classes/0708/GeomAndTop/Maxwell.pdf –  chhan92 Jan 12 at 3:14
@Christopher White please read my above comment –  chhan92 Jan 12 at 3:35

Scheck's books are mathematically much more precise than the average physicist's textbook.

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I have taken look at that book and it does not seem to prove Maxwell's equation from Biot-Savart's law and etc (as how Maxwell would approach from historical point of view?) –  chhan92 Jan 12 at 3:13
William: I think you're right, but the thing is you can leverage the fact that you're on a four-manifold to get an incredibly beautiful formulation of electrodynamics. IIRC (I don't have MTW in front of me) you write the Faraday tensor--actually a differential form--$F$, in terms of which Maxwell's equations become $$F^{ij}_{;j} = J^i$$ and $F^{i[j}_{;k]} = (dF)^{ij}_{k} = 0$, where I write $d$ for the exterior derivative. This can be further simplified by noting that the second implies (I think) that $F = dA$ for some 1-form $A$, the vector potential. –  Christopher White Dec 7 '12 at 17:06