Man every time I try to read something that, like, uses multivariate calculus in anger, like these undergraduate course notes deriving the shallow water equation, I remember how much I don't really know, deep down in my guts, that sort of engineering-style math that involves all those, how you say, numbers. And divs and grads and curls, and all that. I can follow it formally, to be sure, but it always passes through only the shallower parts of my brain. Or maybe it's just specifically the phenomenon of advection in fluid dynamics that makes me feel extra derp. Not sure.