The vector operators Gradient, Divergence and Curl can be expressed in generic curvilinear coordinates. These can then be specialized in any other coordinate system of preference through the definition of three functions that appear in all the curvilinear forms. For Cartesian coordinates, Spherical coordinates and Cylindrical coordinates, the functions are the following.
| Function | Cartesian | Spherical | Cylindrical |
|---|---|---|---|
| 1 | 1 | 1 | |
| 1 | |||
| 1 | 1 |