




Given a vector field, v(x, y ,z):
v(x, y ,z) = v_{1}(x, y, z)i + v_{2}(x, y, z)j + v_{3}(x, y, z)k
Each of its 3 components has derivatives with respect to each of the 3 variables,
which gives a total of 9 first derivatives;
The Divergence of v, is a combination of these of particular importance; it
is a scalar function; it is defined as the dot product of the vector operator
or equivalently
with the vector v.
Thus we have:
This vector operator is often written as, and called "del". The divergence is written as either (div v) or (v) and is also called "del dot v".