The derivation of material balance difference equations in more than one space
dimension very closely parallels the derivation for the one space variable
case of the previous section.
For the case of two space variables, we assume that some material M has a
spatial density given by 
.
Again, for simplicity, we begin by assuming that density
is related to a field variable 
by a linear constitutive equation
of the form
We assume the flow of material M to be down-gradient with respect to u.
That is, the flux 
is given by
or
