This was one nice thing about studying physics, most of the math we learned was motivated by some application. I think my first exposure to div and curl was usi

This was one nice thing about studying physics, most of the math we learned was motivated by some application. I think my first exposure to div and curl was using the analogy of fluids flowing in the plane. Intuitively, divergence is how much fluid is being created (or destroyed) at a point, curl is how much a waterwheel would spin if placed at a point.