(* heatkernel.nb *)

G[x_,t_]:=Exp[-x^2/(4*t)]/(2*Sqrt[Pi*t])

g=Plot[Table[G[x,t],{t,0.1,1.0,0.1}],{x,-5,5},PlotRange->All]

Manipulate[Plot[G[x,t],{x,-5,5},PlotRange->{0,3}],{t,0.01,2}]

Manipulate[Plot[G[x,1/invt],{x,-2,2},PlotRange->All],{invt,1,1000}]