The Wave Equation

Needs["Calculus`VectorAnalysis`"]

The wave equation without damping in Cartesian coordinates is

(d/dt)^2 u = Div[ c^2 Grad[u]]

In[5]=
waveCartesian := 

	D[u[x,y,t],{t,2}] == Div[c^2 Grad[u[x,y,t]]]
waveCartesian

Out[5]=
 (0,0,2)              2  (0,2,0)             2  (2,0,0)

u       [x, y, t] == c  u       [x, y, t] + c  u       [x, y, t]

The superscripts on u represent partial derivatives. For example, u^(2,0,0) is the second derivative with respect to x.