An important reference to add the already good answers is the two volume set: * Paul Bamberg, Shlomo Sternberg *"A course in mathematics for students in physics"* ([Vol 1](https://www.amazon.com/Course-Mathematics-Students-Physics/dp/0521406498), [Vol 2](https://www.amazon.com/Course-Mathematics-Students-Physics/dp/0521406501/)) 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.