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7.1 Definition of Divergence

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:

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".