拡散方程式(偏微分方程式)の解
樋口三郎 https://hig3.net

Animate[Plot[1/Sqrt[2Pi t]Exp[-x^2/(2*t)],{x,-5,5},PlotRange->{{-5,5},{0,0.5}},AxesLabel->{"x","u"}],{t,1,4}]

a=Manipulate[Plot[1/Sqrt[2Pi t]Exp[-x^2/(2*t)],{x,-5,5},PlotRange->{{-5,5},{0,0.5}},AxesLabel->{"x","u"}],{t,1,4}]

u(x,t)=(1/(Sqrt[2π t]))(e^(-((x^2)/(2t))))

Plot3D[1/Sqrt[2Pi 1/4 t]Exp[-x^2/(2 1/4 t)],{x,-5,5},{t,1,21},PlotRange->{{-5,5},{1,20},{0,0.8}},BoxRatios->{1,2,0.8},PlotStyle->{Opacity[0.4]},AxesLabel->{Style["x",Italic,20],Style["t",Italic,20],Style["u",Italic,20]},PlotPoints->20]

ImageReflect[ContourPlot[1/Sqrt[2Pi 1/4 t]Exp[-x^2/(2 1/4 t)],{x,-5,5},{t,1,21},PlotRange->{{-5,5},{1,20},{0,0.8}},AspectRatio->2,FrameLabel->{"x","t"}]]

Plot3D[1/Sqrt[2Pi 1/4 t]Exp[-x^2/(2 1/4 t)],{x,-5,5},{t,1,21},PlotRange->{{-5,5},{1,20},{0,0.8}},BoxRatios->{1,2,0.8},PlotStyle->{Opacity[0.4]},AxesLabel->{Style["x",Italic,20],Style["t",Italic,20],Style["u",Italic,20]},ViewPoint->{0,Infinity,0},PlotPoints->20]

Plot3D[1/Sqrt[2Pi 1/4 t]Exp[-x^2/(2 1/4 t)],{x,-5,5},{t,1,21},PlotRange->{{-5,5},{1,20},{0,0.8}},BoxRatios->{1,2,0.8},PlotStyle->{Opacity[0.4]},AxesLabel->{Style["x",Italic,20],Style["t",Italic,20],Style["u",Italic,20]},ViewPoint->{Infinity,0,0},PlotPoints->20]