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.|
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Given a vector field, v(x, y ,z):
v(x, y ,z) = v1(x, y, z)i + v2(x, y, z)j + v3(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:
,
and called "del". The divergence is written as either (div v) or (
v)
and is also called "del dot v".