Mr. Integral
Math notes/Calculus III/Vector Calculus

Divergence and Curl — Cheat sheet

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Core rule

div⁡F=Px+Qy+Rz.\operatorname{div}\mathbf F=P_x+Q_y+R_z. curl⁡F=(Ry−Qz,Pz−Rx,Qx−Py).\operatorname{curl}\mathbf F=(R_y-Q_z,P_z-R_x,Q_x-P_y).

Watch for

Divergence is scalar expansion; curl is vector rotation. Neither equals speed.