
(a) By using a small cube centered on a point (x, y, z) of dimensions (Δx, Δy, Δz), explain what this theorem says about the matter in and around the cube and what you can say about how it is moving through the various sides of the cube. Be explicit in showing the relation between your statements and the mathematical expresions.
(b) For an arbitrary vector field (about which you know nothing except that it is continuous and differentiable) describe in words what the value of the divergence of the field at a point (x, y, z),
is telling you about the field.
Last revision 28. December, 2010.