Heat Equation Example from Class

>	restart:with(plots):

Warning, the name changecoords has been redefined

>	c:=proc(k) #This procedure computes the coeffients.  40/((2*k-1)*Pi) end;

>	c(1);c(2);c(21);

First we just use 10 nonzero tems. Remember f(x) = 10 is the initial temp distrabution. I did t=0 to 1 unit with 50 frames.

>	m:=10; # Set number of terms to use.

>	animate((sum((c(k)*sin((2*k-1)*Pi*x)*exp(-(2*k-1)^2*Pi^2*t) ),k=1..m)), x=0..1, t=0..1,frames=50, color=green);

Next I'll use m=25 to use the first 25 nonzero terms.

>

m:=25;

>	animate((sum((c(k)*sin((2*k-1)*Pi*x)*exp(-(2*k-1)^2*Pi^2*t) ),k=1..m)), x=0..1, t=0..1,frames=50, color=green);

The result is not really  much better. Next I'll display some indiviual frames for the m=10 case.

>	m:=10: t:=0:

>	plot(sum(  c(k)*sin((2*k-1)*Pi*x)*exp(-(2*k-1)^2*Pi^2*t)   ,k=1..m), x=0..1);

>

t:=0.01:

>	plot(sum(  c(k)*sin((2*k-1)*Pi*x)*exp(-(2*k-1)^2*Pi^2*t)   ,k=1..m), x=0..1,yview=0..10.5);

>

t:=0.05:

>	plot(sum(  c(k)*sin((2*k-1)*Pi*x)*exp(-(2*k-1)^2*Pi^2*t)   ,k=1..m), x=0..1,yview=0..10.5);

>

t:=0.1:

>	plot(sum(  c(k)*sin((2*k-1)*Pi*x)*exp(-(2*k-1)^2*Pi^2*t)   ,k=1..m), x=0..1,yview=0..10.5);

>