(*						      *)
(* Numerical Mathematics and Computing, Fifth Edition *)
(* Ward Cheney & David Kincaid		              *)
(* Brooks/Cole Publ. Co.			      *)
(* (c) 2003                                           *)
(* No warranties implied or expressed.	              *)
(* File: heat   				      *)
(* PDE: solve heat eqn & plot			      *)
soln = NDSolve[
{D[u[x,t],x,x] == D[u[x,t],t],
u[0,t] == 0, u[1,t] == 0, u[x,0] == Sin[Pi*x]}, u, {x, 0, 1}, {t, 0, .5}];
Plot3D[Evaluate[u[x,t] /. First[soln]], {x, 0, 1}, {t, 0, .5},
PlotPoints->30,PlotRange->All]
ContourPlot[Evaluate[u[x,t] /. First[soln]], {x, 0, 1}, {t, 0, .5},
PlotPoints->30,Contours->30,ContourLines->False,ColorFunction->Hue,
PlotRange->All]