Standing Wave Solution to Wave Equation

Manipulate[Plot[Sin[x]*Cos[2*Pi*t],{x,-10,10},PlotRange->{-1.1,1.1}],{t,0,1}]

Fundamental Solution to Heat Equation

Manipulate[Plot[(1/Sqrt[4*Pi*t])*Exp[-(x^2)/(4*t)],{x,-100,100},PlotRange->{0,0.13}],{t,5,75}]