Sorry to throw some technical math on you, but it's been bothering me a while.
So I'm a third year undergrad, and have thoroughly been using gradients, curls, and divergences now. I know that the purpose of the gradient is to measure the rate of maximum change, and on a contour map, it would be the steepest descent down a mountain. But what about the divergence and curl? What is the conceptual significance of them? I asked my prof, and he kind of swept it under the rug, saying divergence has to deal with rate of change, and curl has to do with rotational motion, but if there are better answers out there I would really appreciate it.
Thanks in advance.