Section 2.1 #4

In this problem, we find the fundamental solution for the heat equation in two spatial variables.  The 2D fundamental solution is a product of two 1D fundamental solutions.

g[x_,y_,t_,k_]=Exp[-(x^2+y^2)/4/k/t]/4/Pi/k/t

Plot3D[g[x,y,0.01,1],{x,-5,5},{y,-5,5},PlotRange->All,PlotPoints->25,MeshFunctions->(#3&)]

Animate[Plot3D[g[x,y,t,1],{x,-5,5},{y,-5,5},PlotRange->{0,10},PlotPoints->25,MeshFunctions->(#3&)],{t,0,0.1},AnimationRunning->False]