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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 21 "Rectangular membrane." }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(plots):with(linalg):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "chi:=(a,b,x)->Heaviside(x
-a)*Heaviside(b-x):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Dimensions
 of the membrane." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "a:=2;b
:=1;xrange:=0..a:yrange:=0..b:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
aG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 21 "Initial displacement." }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 40 "f:=(x,y)->0.5*chi(0,a/2,x)*chi(0,b/2,y);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6$%\"xG%\"yG6\"6$%)operatorG%&
arrowGF),$*&-%$chiG6%\"\"!,$%\"aG#\"\"\"\"\"#9$F6-F06%F2,$%\"bGF59%F6$
\"\"&!\"\"F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "setoption
s3d(scaling=constrained,style=patchcontour);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 33 "plot3d(f(x,y),x=xrange,y=yrange);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 25 "Double Fourier expansion." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "m:=5;n:=5;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"mG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"
\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "B:=matrix(m,n,0):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "for i from 1 to m by 1 do
 for j from 1 to n by 1 do B[i,j]:=(4/(a*b))*int(int(f(x,y)*sin(i*Pi*x
/a)*sin(j*Pi*y/b),x=xrange),y=yrange);od;od;" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 37 "Speed of propagation and eigenvalues." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "c:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"cG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "lambda:=c*Pi
*sqrt((ii/a)^2+(jj/b)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'lambda
G,$*&%#PiG\"\"\",&*$%#iiG\"\"#F(*$%#jjGF,\"\"%#F(F,F0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "h:=(x,y,t)->sum(sum(B[ii,jj]*sin(ii
*Pi*x/a)*sin(jj*Pi*y/b)*cos(lambda*t),ii=1..m),jj=1..n);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"hG:6%%\"xG%\"yG%\"tG6\"6$%)operatorG%&arrowG
F*-%$sumG6$-F/6$**&%\"BG6$%#iiG%#jjG\"\"\"-%$sinG6#**F7F9%#PiGF99$F9%
\"aG!\"\"F9-F;6#**F8F9F>F99%F9%\"bGFAF9-%$cosG6#*&%'lambdaGF99&F9F9/F7
;F9%\"mG/F8;F9%\"nGF*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Genera
te frames (dt=time step)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 
"dt:=0.15;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dtG$\"#:!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "plotsetup(plotdevice=`pcx`,p
lotoptions=`height=300,width=300`);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "picfile:=n->plotsetup(plotoutput=cat(`/data/gokhman/p
ic_`,1000+n,`.pcx`)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pi
cfile(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot3d(f(x,y),
x=xrange,y=yrange);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "for \+
nn from 1 to 40 by 1 do picfile(nn);plot3d(h(x,y,nn*dt),x=xrange,y=yra
nge);od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 \+
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