Carlos Herrera 💙❤️🩷

The Five Differential Operators of Physics Five operators built from one symbol, nabla, all moving at once. Divergence: div F = dFx/dx + dFy/dy + dFz/dz, the net flux out of a tiny closed surface (source or sink strength). Gradient: grad phi = (dphi/dx, dphi/dy, dphi/dz) points to the steepest increase of phi, always at a right angle to the contour lines, and is longest where they are tightest. Curl: curl F measures the spin of the field around a point. The vector stands on the axis of the whirl, and flips when the whirl reverses. Laplacian: the sum of the second derivatives. On the bowl z = x^2 + y^2 the Laplacian is 4, so the average around any circle of radius r sits exactly r^2 above its centre. D'Alembertian: box F = (1/c^2) d^2F/dt^2 - Laplacian F. A wave running at speed c makes it zero, which is why it appears in the wave equation and in relativity.