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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "# Problem 3.5-13, he
at equation," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f1:=x->33*x
;f2:=x->33*(Pi-x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "f:=x-
>piecewise(x<0,0,x<Pi/2,f1(x),x<Pi,f2(x),0):\nu1:=x->-50*x/Pi+100;'f(x
)'=eval(f(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "assume(n,
integer):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "b[n]:=simplify
((2/Pi)*int((f(x)-u1(x))*sin(n*x),x=0..Pi));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 19 "b:=unapply(b[n],n);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 75 "u2:=(x,t)->sum(b(n)*sin(n*x)*exp(-n^2*t),n=1..50);
\nu:=(x,t)->u1(x)+u2(x,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
36 "u(0,0,20);u(Pi,0,20);b(1),b(2),b(3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "plot3d(u(x,t),x=0..Pi,t=0..1.5,axes=boxed);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "#u(x,0);" }}}}{MARK "10" 0 }
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