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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 38 "Graph of Solution of the Heat E
quation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
29 "I will graph the solution of " }{XPPEDIT 18 0 "u[xx] = u[t];" "6#/
&%\"uG6#%#xxG&F%6#%\"tG" }{TEXT -1 0 "" }{TEXT -1 5 " for " }{XPPEDIT 
18 0 "x;" "6#%\"xG" }{TEXT -1 11 " in (0,1), " }{XPPEDIT 18 0 "0 < t;
" "6#2\"\"!%\"tG" }{TEXT -1 6 " with " }{XPPEDIT 18 0 "u(0,t) = 0;" "6
#/-%\"uG6$\"\"!%\"tGF'" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "u(1,t) = 0
;" "6#/-%\"uG6$\"\"\"%\"tG\"\"!" }{TEXT -1 5 " for " }{XPPEDIT 18 0 "0
 < t;" "6#2\"\"!%\"tG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "u(x,0) = si
n(2*Pi*x)-sin(5*Pi*x);" "6#/-%\"uG6$%\"xG\"\"!,&-%$sinG6#*(\"\"#\"\"\"
%#PiGF/F'F/F/-F+6#*(\"\"&F/F0F/F'F/!\"\"" }{TEXT -1 5 " for " }
{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 10 " in [0,1]." }{TEXT -1 17 " \+
 The solution is" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 69 "u := (x,t) -> exp(-4*Pi^2*t)*sin(2*Pi*x)-exp(-
25*Pi^2*t)*sin(5*Pi*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "
plot3d(u(x,t),x=0..1,t=0..0.05,axes=normal);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0
" 38 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }