Gradient, divergence, curl, Laplacian কী?

For a scalar field $f$ and a vector field $\vect A$, in Cartesian coordinates with the symbolic vector $\vect\nabla = (\partial_x, \partial_y, \partial_z)$:

and $\Delta\vect A$ is the Laplacian taken on each Cartesian component. Their meaning is independent of coordinates: $\operatorname{\vect{grad}}f \cdot\dd\vect l = \dd f$ is the change of $f$ along $\dd\vect l$; $\operatorname{div} \vect A$ is the outgoing flux of $\vect A$ through the surface of a small volume, per unit volume; $\operatorname{\vect{curl}}\vect A\cdot\vect n$ is the circulation of $\vect A$ around a small loop of normal $\vect n$, per unit area.