We derive the divergence theorem over a large volume V by dividing it into a large number of very tiny volumes. For each tiny volume ∆V, the definition of the divergence tells us that
where the surface integral here is over the surface surrounding ∆V. If we now add up all of the tiny volumes in the large volume V, the sum of the terms on the left in the above equation becomes the left side of the divergence on the previous card.
