I bought the book (a long time ago) thinking I was going to get something exactly like what the OP video is: a mathematical explanation of what the tools do, with some intuitive link between - say - the formula for div and why it measures how much a vector field does indeed "diverge" locally.

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.