Advanced Mathematics for Engineers and Scientists/The Front Cover

Common Operators
Operators are shown applied to the scalar $$u(x_1, x_2, \cdots, x_n)$$ or the vector field $$\mathbf{v}(x_1, x_2, \cdots, x_n) = (v_1, v_2, \cdots, v_n)\,$$.

3D Operators in Different Coordinate Systems
Cartesian representations appear in the table above. The $$(r, \theta, \phi) = (\mathrm{distance, azimuth, colatitude})$$ convention is used for spherical coordinates.