An important reference to add the already good answers is the two volume set:
It is based on a Harvard course given by the authors back in the 80's, and it is basically a book on the calculus of differential forms geared towards physical applications: gaussian optics, electrical networks, electrostatics, magnetostatics, Maxwell's equations, thermodynamics are some of the topics discussed in the book in this setting.
Chapter 19 on Volume 2 is exactly about Maxwell's equations in differential form.