There's also a book on the subject called "Div, Grad, Curl and all that"
https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161
which I would highly recommend to physics-minded folks, but would not recommend at all to maths-minded folks.
https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161
which I would highly recommend to physics-minded folks, but would not recommend at all to maths-minded folks.
Why not?
Instead, the whole book tries to explain the 3 tools using electrostatics as an intuitive justification for how they behave. Ugh.
To me, the way electromagnetic fields behave is no particularly intuitive or natural, and the way I do - sort of - manage to understand Maxwell's equations is because I have an intuitive feel for what grad, div and curl do to vector fields.