In Cartesian coordinates:

                  ................................................(1.44)

In cylindrical coordinates:

                 ...........................................(1.45)

and in spherical polar coordinates:

                 .................................(1.46)

Gradient of a Scalar function:

Let us consider a scalar field V(u,v,w) , a function of space coordinates.

Gradient of the scalar field V is a vector that represents both the magnitude and direction of the maximum space rate of increase of this scalar field V.