>    restart;

>    t:=0: u := (x,y) -> Sum( Sum(sin(2*sqrt(4*n*n + m*m)*t)/(n*m*sqrt(4*n*n+m*m)) * sin(2*n*x) * sin(m*y) , n=1..15), m=1..15);
plot3d( u(x,y), x=0..0.5*Pi, y=0..Pi, labels =[`x`, `y`, `time = 1`], axes=FRAMED, style=patch);

u := proc (x, y) options operator, arrow; Sum(Sum(sin(2*sqrt(4*n*n+m*m)*t)/n/m/sqrt(4*n*n+m*m)*sin(2*n*x)*sin(m*y),n = 1 .. 15),m = 1 .. 15) end proc

[Maple Plot]

>    g := (x,y) -> (Pi/2 -x)*(Pi-y); plot3d( g(x,y), x=0..0.5*Pi, y=0..Pi, labels =[`x`, `y`, `time = 1`], axes=FRAMED, style=patch);

g := proc (x, y) options operator, arrow; (1/2*Pi-x)*(Pi-y) end proc

[Maple Plot]

>    t:=1: u := (x,y) -> Sum( Sum(sin(2*sqrt(4*n*n + m*m)*t)/(n*m*sqrt(4*n*n+m*m)) * sin(2*n*x) * sin(m*y) , n=1..15), m=1..15);
plot3d( u(x,y), x=0..0.5*Pi, y=0..Pi, labels =[`x`, `y`, `time = 1`], axes=FRAMED, style=patch);

u := proc (x, y) options operator, arrow; Sum(Sum(sin(2*sqrt(4*n*n+m*m)*t)/n/m/sqrt(4*n*n+m*m)*sin(2*n*x)*sin(m*y),n = 1 .. 15),m = 1 .. 15) end proc

[Maple Plot]

>    t:=5: u := (x,y) -> Sum( Sum(sin(2*sqrt(4*n*n + m*m)*t)/(n*m*sqrt(4*n*n+m*m)) * sin(2*n*x) * sin(m*y) , n=1..4), m=1..4);
plot3d( u(x,y), x=0..0.5*Pi, y=0..Pi, labels =[`x`, `y`, `time = 1`], axes=FRAMED, style=patch);

u := proc (x, y) options operator, arrow; Sum(Sum(sin(2*sqrt(4*n*n+m*m)*t)/n/m/sqrt(4*n*n+m*m)*sin(2*n*x)*sin(m*y),n = 1 .. 4),m = 1 .. 4) end proc

[Maple Plot]

>    t:=10: u := (x,y) -> Sum( Sum(sin(2*sqrt(4*n*n + m*m)*t)/(n*m*sqrt(4*n*n+m*m)) * sin(2*n*x) * sin(m*y) , n=1..4), m=1..4);
plot3d( u(x,y), x=0..0.5*Pi, y=0..Pi, labels =[`x`, `y`, `time = 1`], axes=FRAMED, style=patch);

u := proc (x, y) options operator, arrow; Sum(Sum(sin(2*sqrt(4*n*n+m*m)*t)/n/m/sqrt(4*n*n+m*m)*sin(2*n*x)*sin(m*y),n = 1 .. 4),m = 1 .. 4) end proc

[Maple Plot]

>    t:=12: u := (x,y) -> Sum( Sum(sin(2*sqrt(4*n*n + m*m)*t)/(n*m*sqrt(4*n*n+m*m)) * sin(2*n*x) * sin(m*y) , n=1..4), m=1..4);
plot3d( u(x,y), x=0..0.5*Pi, y=0..Pi, labels =[`x`, `y`, `time = 1`], axes=FRAMED, style=patch);

u := proc (x, y) options operator, arrow; Sum(Sum(sin(2*sqrt(4*n*n+m*m)*t)/n/m/sqrt(4*n*n+m*m)*sin(2*n*x)*sin(m*y),n = 1 .. 4),m = 1 .. 4) end proc

[Maple Plot]

>    t:=18: u := (x,y) -> Sum( Sum(sin(2*sqrt(4*n*n + m*m)*t)/(n*m*sqrt(4*n*n+m*m)) * sin(2*n*x) * sin(m*y) , n=1..4), m=1..4);
plot3d( u(x,y), x=0..0.5*Pi, y=0..Pi, labels =[`x`, `y`, `time = 1`], axes=FRAMED, style=patch);

u := proc (x, y) options operator, arrow; Sum(Sum(sin(2*sqrt(4*n*n+m*m)*t)/n/m/sqrt(4*n*n+m*m)*sin(2*n*x)*sin(m*y),n = 1 .. 4),m = 1 .. 4) end proc

[Maple Plot]

>