If the surface integral is carried out over a closed surface, then we write

Volume Integrals:

We define or as the volume integral of the scalar function f(function of spatial coordinates) over the volume V. Evaluation of integral of the form can be carried out as a sum of three scalar volume integrals, where each scalar volume integral is a component of the vector

The Del Operator :

The vector differential operator was introduced by Sir W. R. Hamilton and later on developed by P. G. Tait.

Mathematically the vector differential operator can be written in the general form as:

                      .................................(1.43)