Module 1 : A Crash Course in Vectors
Lecture 4 : Gradient of a Scalar Function
Divergence of a Vector Field :
  Divergence of a vector field $\vec F$ is a measure of net outward flux from a closed surface $S$ enclosing a volume $V$, as the volume shrinks to zero.
  where $\Delta V$ is the volume (enclosed by the closed surface $S$) in which the point P at which the divergence is being calculated is located. Since the volume shrinks to zero, the divergence is a point relationship and is a scalar.
  Consider a closed volume $V$ bounded by $S$. The volume may be mentally broken into a large number of elemental volumes closely packed together. It is easy to see that the flux out of the boundary $S$ is equal to the sum of fluxes out of the surfaces of the constituent volumes. This is because surfaces of boundaries of two adjacent volumes have their outward normals pointing opposite to each other. The following figure illustrates it.
 
   
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