SetDirectory[$HomeDirectory<>"/Documents/handouts/math467/Maximum"]

Maximum Principle

Graphics[{GrayLevel[2/3],Rectangle[{0.1,0},{1.1,1}],Black,Text["R",{1.1,1}/2],Text["S",{0.05,1/2}],Thickness[1/100],CapForm["Butt"],Line[{{0.1,1},{0.1,0},{1.1,0},{1.1,1}}],PointSize[Large],Point[{1,2}/3],Text["((Subscript[x, 0]), (Subscript[t, 0]))",{1,2.1}/3,{-1,-1}]},AxesOrigin->{0,0},Axes->True,AxesLabel->{"x","t"},Ticks->{{{0.1,"0"},{1.1,"L"}},{{1,"T"}}}]

Export["maxregion.pdf",%,"PDF"]

Export["maxregion.eps",%%,"EPS"]

Example

f[x_]:=6Sin[π x/3]+2Sin[π x]

Plot[f[x],{x,0,3},AxesLabel->{"x","f(x)"}]

Export["example01.pdf",%,"PDF"]

Export["example01.eps",%%,"EPS"]

f[3/4]

f[3/2]

u[x_,t_]:=6Exp[-(π^2)t]Sin[π x/3]+2Exp[-9(π^2)t]Sin[π x]

Plot3D[u[x,t],{x,0,3},{t,0,1/10},AxesLabel->{"x","t","u(x,t)"},PlotRange->All]

Export["example01surf.pdf",%,"PDF"]

Export["example01surf.eps",%%,"EPS"]