Hi,

is there a textbooks that explains the maxwell equations in differential form?

What I understood so far is, that the $E$ and $B$ fields can be assembled to a differential 2 Form $F$, and the Maxwell Equations can be written quite nicely with the Hodge $*$ and the exterior deriative $d$. Going further the equations can be derived as an Euler Lagrange (or Yang Mills?) equation from a connection of a fibre bundle.

I am searching for a book that describes how the geometric entities are mapped to the physical entities with a focus on mathematical exactness.

Thanks