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); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CGf*6#%\"nG6\"6$%)operatorG
%&arrowGF(,$,$-%$intG6$*&-%#f1G6#%\"xG\"\"\"-%$sinG6#**%#PiGF69$F6F5F6
%\"LG!\"\"F6/F5;\"\"!F=*&\"\"#F6F=F>F6F(F(F(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 44 "Q:=n->2/L*int(f2(x)*sin(Pi*n*x/L), x=0..L); " }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QGf*6#%\"nG6\"6$%)operatorG%&arrow
GF(,$,$-%$intG6$*&-%#f2G6#%\"xG\"\"\"-%$sinG6#**%#PiGF69$F6F5F6%\"LG!
\"\"F6/F5;\"\"!F=*&\"\"#F6F=F>F6F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 29 "\300\355\340\353\356\343\350\367\355\356 \357\356\353\363
\367\350\354 \344\353\377 v(x,y)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "Cv:=n->2/Ly*int(f1(y)*sin(Pi*n*y/Ly), y=0..Ly); " }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#CvGf*6#%\"nG6\"6$%)operatorG%&arrow
GF(,$,$-%$intG6$*&-%#f1G6#%\"yG\"\"\"-%$sinG6#**%#PiGF69$F6F5F6%#LyG!
\"\"F6/F5;\"\"!F=*&\"\"#F6F=F>F6F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "Qv:=n->2/Ly*int(f3(y)*sin(Pi*n*y/Ly), y=0..Ly);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#QvGf*6#%\"nG6\"6$%)operatorG%&arrow
GF(,$,$-%$intG6$*&-%#f3G6#%\"yG\"\"\"-%$sinG6#**%#PiGF69$F6F5F6%#LyG!
\"\"F6/F5;\"\"!F=*&\"\"#F6F=F>F6F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 63 "*) \317\360\356\342\345\344\270\354 \342\350\347\363\340
\353\350\347\340\366\350\376 C(n) \350 Q(n) \361 \363\367\345\362\356
\354 \342\373\341\356\360\340 \357\340\360\340\354\345\362\360\356\342
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L:=2*q:Ly:=2*b:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "\350 \357\356\361\353\345 \363\357
\360\356\371\345\355\350\377" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 50 "C(n) := 2*q^2*G*(2+(-1)^n*(Pi^2*n^2-2))/Pi^3/n^3; " }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>-%\"CG6#%\"nG,$*.\"\"#\"\"\"%\"qGF*%\"GGF+,&F*F
+*&)!\"\"F'F+,&*&)%#PiGF*F+)F'F*F+F+F*F1F+F+F+F5!\"$F'F7F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Q(n):=2*q^2*G*(2+(-1)^n*(Pi^2*n^2-2
))/Pi^3/n^3+2*G*b^2*((-1)^n-1)/Pi/n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>-%\"QG6#%\"nG,&*.\"\"#\"\"\"%\"qGF*%\"GGF+,&F*F+*&)!\"\"F'F+,&*&)%#
PiGF*F+)F'F*F+F+F*F1F+F+F+F5!\"$F'F7F+*.F*F+F-F+%\"bGF*,&F0F+F+F1F+F5F
1F'F1F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "\300\355\340\353\356
\343\350\367\355\356 \344\353\377 Qv(n), \355\356 \361 \361\356\356
\362\342\345\362\361\362\342\363\376\371\345\351 \347\340\354\345\355
\356\351 (\342 1-\354 \361\353\340\343\340\345\354\356\354 q->b \350 \+
\342\356 " }}{PARA 0 "" 0 "" {TEXT -1 12 "2-\354 - b->q)." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "Qv(n):=2*b^2*G*(2+(-1)^n*(Pi^2*n^2-
2))/Pi^3/n^3+  2*G*q^2*((-1)^n-1)/Pi/n;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>-%#QvG6#%\"nG,&*.\"\"#\"\"\"%\"bGF*%\"GGF+,&F*F+*&)!\"\"F'F+,&*
&)%#PiGF*F+)F'F*F+F+F*F1F+F+F+F5!\"$F'F7F+*.F*F+F-F+%\"qGF*,&F0F+F+F1F
+F5F1F'F1F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "\302\342\345\344
\345\354 \356\341\356\347\355\340\367\345\355\350\377: Cn=C(n), Qn=Q(n
) \344\353\377 \363\344\356\341\361\362\342\340 \361\350\354\342\356
\353\374\355\373\365 \342\373\367\350\361\353\345\355\350\351. " }}
{PARA 0 "" 0 "" {TEXT -1 85 "\304\353\377 \342\373\367\350\361\353\345
\355\350\377 \352\356\375\364\364\350\366\350\345\355\362\356\342 An, \+
Bn \363\360\340\342\355\345\355\350\377 (6) \361\356\361\362\340\342
\353\377\345\354 \361\350\361\362\345\354\363 \344\342\363\365 \363
\360\340\342\355\345\355\350\351  " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "ur1:=An+Bn=Cn;  " }{TEXT -1 12 "- \344\353\377 y = 0.
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ur1G/,&%#AnG\"\"\"%#BnGF(%#CnG
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "ur22:=An*exp(r(n)*Ly)+B
n*exp(-r(n)*Ly)=Qn; " }{TEXT -1 6 "- \344\353\377 " }{TEXT 327 1 "y" }
{TEXT -1 6 " = Ly." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ur22G/,&*&%#A
nG\"\"\"-%$expG6#**%#PiGF)%\"nGF)%\"qG!\"\"%\"bGF)F)F)*&%#BnGF)-F+6#,$
F-F1F)F)%#QnG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "\300\355\340\353
\356\343\350\367\355\356 \344\353\377 v(x,y)" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 15 "uv1:=Av+Bv=Cvn;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%$uv1G/,&%#AvG\"\"\"%#BvGF(%$CvnG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "uv22:=Av*exp(ry(n)*L)+Bv*exp(-ry(n)*L)=Qvn;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%uv22G/,&*&%#AvG\"\"\"-%$expG6#**%#PiGF)%
\"nGF)%\"bG!\"\"%\"qGF)F)F)*&%#BvGF)-F+6#,$F-F1F)F)%$QvnG" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 77 "\314\356\346\355\356 \342\345\361\362\350
 \363\357\360\356\371\345\355\350\345 \357\360\350 \347\340\357\350
\361\350 \342\362\356\360\356\343\356 \363\360\340\342\355\345\355\350
\377 \357\363\362\345\354 \357\356\344\361\362\340\355\356\342\352\350
. \302\342\345\344\345\354 " }}{PARA 0 "" 0 "" {TEXT -1 45 "\355\356
\342\363\376 \357\345\360\345\354\345\355\355\363\376 R = Pi*n/L*Ly. \+
\322\356\343\344\340 \357\356\353\363\367\350\354" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 34 "ur2:=subs(r(n)*Ly=R,ur22);r(n)*Ly;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$ur2G/,&*&%#AnG\"\"\"-%$expG6#%\"RGF)F)*&%
#BnGF)-F+6#,$F-!\"\"F)F)%#QnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**%#P
iG\"\"\"%\"nGF%%\"qG!\"\"%\"bGF%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "uv2:=subs(ry(n)*L=Rv,uv22);ry(n)*L;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%$uv2G/,&*&%#AvG\"\"\"-%$expG6#%#RvGF)F)*&%#BvGF)-F
+6#,$F-!\"\"F)F)%$QvnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**%#PiG\"\"
\"%\"nGF%%\"bG!\"\"%\"qGF%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "
\320\345\370\340\345\354 \361\350\361\362\345\354\363 \344\342\363\365
 \363\360\340\342\355\345\355\350\351 \350 \355\340\365\356\344\350
\354 An, Bn" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "svv:=solve(
\{ur1,ur2\},[An,Bn]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$svvG7#7$/
%#AnG,$*&,&%#QnG!\"\"*&%#CnG\"\"\"-%$expG6#,$%\"RGF-F0F0F0,&-F26#F5F0F
1F-F-F-/%#BnG*&F6F-,&*&F/F0F7F0F0F,F-F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "`N9:=convert(svv,'list'); N9[1][2];`:`op:nops:`:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "slv:=solve([uv1,uv2],\{Av,Bv
\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$slvG<$/%#AvG,$*&,&%$QvnG!
\"\"*&%$CvnG\"\"\"-%$expG6#,$%#RvGF,F/F/F/,&-F16#F4F/F0F,F,F,/%#BvG*&F
5F,,&*&F.F/F6F/F/F+F,F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "*) \+
\302\342\345\344\345\354 \347\340\360\340\355\345\345 \357\356\344\361
\362\340\355\356\342\356\367\355\373\345 \347\355\340\367\345\355\350
\377  \352\356\375\364\364\350\366\350\345\355\362\356\342, \347\340
\357\350\361\373\342\340\377 \350\365 \352\340\352 " }{TEXT 320 2 "An
" }{TEXT -1 3 " \350 " }{TEXT 319 2 "Bn" }{TEXT -1 1 "." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 72 "\316\357\377\362\374 \344\353\377 \363
\357\360\356\371\345\355\350\377 \342\356\361\357\356\353\374\347\363
\345\354\361\377 \357\356\344\361\362\340\355\356\342\352\356\351, \+
\342\373\341\350\360\340\377 \356\344\355\363 \350\347 \364\356\360
\354\363\353: " }}{PARA 0 "" 0 "" {TEXT -1 85 "exp(z)-exp(-z)=2sinh(z)
, exp(z)+exp(-z)=2cosh(z), (exp(z)^2+1)/(exp(z)^2-1)=coth(z), " }}
{PARA 0 "" 0 "" {TEXT -1 49 "exp(z)=sinh(z)+cosh(z), exp(-z)=-sinh(z)+
cosh(z)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "*) \317\360\356\342
\345\360\352\340 \350 \342\373\341\356\360 \347\355\340\367\345\355
\350\351 Ah, Bh" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Ah := -1
/2*(-Qn+Cn*(-sinh(R)+cosh(R)))/sinh(R);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#AhG,$*&#\"\"\"\"\"#F(*&,&%#QnG!\"\"*&%#CnGF(,&-%%sinhG6#%\"RG
F--%%coshGF3F(F(F(F(F1F-F(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 44 "Bh := 1/2*((sinh(R)+cosh(R))*Cn-Qn)/sinh(R);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#BhG,$*&#\"\"\"\"\"#F(*&,&*&,&-%%sinhG6#%\"RGF(-%%c
oshGF0F(F(%#CnGF(F(%#QnG!\"\"F(F.F6F(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 21 "\300\355\340\353\356\343\350\367\355\356 \344\353\377 v(x
,y)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "Avh:=subs(Qn=Qvn,Cn=
Cvn,R=Rv,Ah);Bvh:=subs(Qn=Qvn,Cn=Cvn,R=Rv,Bh);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$AvhG,$*&#\"\"\"\"\"#F(*&,&%$QvnG!\"\"*&%$CvnGF(,&-%%
sinhG6#%#RvGF--%%coshGF3F(F(F(F(F1F-F(F-" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$BvhG,$*&#\"\"\"\"\"#F(*&,&*&,&-%%sinhG6#%#RvGF(-%%coshGF0F(F(
%$CvnGF(F(%$QvnG!\"\"F(F.F6F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
91 "\307\344\345\361\374: R = Pi*n/L*Ly = r(n)*Ly;  L:=2*q, Ly:=2*b, (
q \350 b \354\356\343\363\362 \341\373\362\374 \360\340\342\355\373
\354\350); r(n)=Pi*n/L: " }}{PARA 0 "" 0 "" {TEXT -1 69 "ry(n)=Pi*n/Ly
: N=infinity:  0<x<L,  0<y<Ly; Rv = Pi*n/Ly*L = ry(n)*L." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 36 "\322\345\357\345\360\374 \347\340\357\350
\370\345\354 \342\373\360\340\346\345\355\350\345 \352\356\354\357\356
\355\345\355\362\373 " }{TEXT 276 1 "W" }{TEXT -1 1 "(" }{TEXT 277 1 "
x" }{TEXT -1 1 "," }{TEXT 278 1 "y" }{TEXT -1 12 ") \350 V(x,y): " }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "\317\360\350\354\345\367\340\355
\350\345. \323 sum \344\356\353\346\355\356 \341\373\362\374 \352\356
\355\352\360\345\362\355\356\345 \347\355\340\367\345\355\350\345 N." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "N:=infinity: " }{TEXT -1 
53 "- \357\360\350 \362\340\352\356\354 \347\340\344\340\355\350\350 N
 Maple \357\360\340\342\350\353\374\355\345\345 \356\357\360\345\344
\345\353\377\345\362 sum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 
"W:=(x,y)->sum((Ah*exp(r(n)*y)+Bh*exp(-r(n)*y))*sin(r(n)*x), n=1..N);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"WGf*6$%\"xG%\"yG6\"6$%)operato
rG%&arrowGF)-%$sumG6$*&,&*&%#AhG\"\"\"-%$expG6#*&-%\"rG6#%\"nGF49%F4F4
F4*&%#BhGF4-F66#,$F8!\"\"F4F4F4-%$sinG6#*&F9F49$F4F4/F<;F4%\"NGF)F)F)
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "\300\355\340\353\356\343\350
\367\355\356 \344\353\377 V(x,y)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 73 "V:=(x,y)->sum((Avh*exp(ry(n)*x)+Bvh*exp(-ry(n)*x))*si
n(ry(n)*y), n=1..N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VGf*6$%\"x
G%\"yG6\"6$%)operatorG%&arrowGF)-%$sumG6$*&,&*&%$AvhG\"\"\"-%$expG6#*&
-%#ryG6#%\"nGF49$F4F4F4*&%$BvhGF4-F66#,$F8!\"\"F4F4F4-%$sinG6#*&F9F49%
F4F4/F<;F4%\"NGF)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "\307\344
\345\361\374: r(n) = Pi*n/(2*q);   ry(n) = Pi*n/(2*b); \322\356\343
\344\340:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "W(x,y); " }
{TEXT -1 35 "- \361\367\345\362 \344\353\350\353\361\377 ___ \361\345
\352. \305\361\362\374 \357\345\367\340\362\374." }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*,^##\"\"\"\"\"#F&%#CnGF&,&-%$expG6#**%#PiGF&%\"qG!\"\"
%\"xGF&^#F&F&F&F&F0F&,&-F+6#,$**F'F0F.F&,&%\"yGF&*&F1F&F2F&F&F&F/F0F&F
&F&F0F0,&-F+6#,$**F'F0F.F&,&F9F0F:F&F&F/F0F&F&F&F0F0" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "V(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#*,^##\"\"\"\"\"#F&%$CvnGF&,&-%$expG6#**%#PiGF&%\"bG!\"\"%\"yGF&^#F&F&
F&F&F0F&,&-F+6#,$**F'F0F.F&,&%\"xGF&*&F1F&F2F&F&F&F/F0F&F&F&F0F0,&-F+6
#,$**F'F0F.F&,&F9F0F:F&F&F/F0F&F&F&F0F0" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 79 "\310\347-\347\340 \355\345\375\364\364\345\352\362\350
\342\355\356\361\362\350 \350\361\357\356\353\374\347\356\342\340\355
\350\377 \355\350\346\345 \357\360\350\342\356\344\350\354\373\365 \+
\342\373\360\340\346\345\355\350\351 Ws, WS, WSu, WnS," }}{PARA 0 "" 
0 "" {TEXT -1 18 "\350\365 \354\356\346\355\356 \356\357\363\361\362
\350\362\374." }}{PARA 0 "" 0 "" {TEXT -1 47 "\316\362\344\345\353\374
\355\356 \347\340\357\350\370\345\354 \362\356, \367\362\356 \361\362
\356\350\362 \357\356\344 \347\355\340\352\356\354 \361\363\354\354
\373" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "Ws:=-1/2*(-Qn+Cn*(
-sinh(R)+cosh(R)))/sinh(R)*exp(1/2*Pi*n/q*y)+1/2*((sinh(R)+cosh(R))*Cn
-Qn)/sinh(R)*exp(-1/2*Pi*n/q*y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#WsG,&*&#\"\"\"\"\"#F(*(,&%#QnG!\"\"*&%#CnGF(,&-%%sinhG6#%\"RGF--%%cos
hGF3F(F(F(F(F1F--%$expG6#,$*,F)F-%#PiGF(%\"nGF(%\"qGF-%\"yGF(F(F(F(F-*
&#F(F)F(*(,&*&,&F1F(F5F(F(F/F(F(F,F-F(F1F--F86#,$*,F)F-F<F(F=F(F>F-F?F
(F-F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "\302 \375\362\350
\365 \364\356\360\354\363\353\340\365 \375\352\361\357\356\355\345\355
\362\373 \354\356\346\355\356 \342\373\360\340\347\350\362\374 \367
\345\360\345\347 \343\350\357\345\360\341\356\353\350\367\345\361\352
\350\345 \364\363\355\352\366\350\350, \350\361\357\356\353\374\347
\363\377" }}{PARA 0 "" 0 "" {TEXT -1 62 "\361\356\356\362\355\356\370
\345\355\350\377: exp(z)=sinh(z)+cosh(z), exp(-z)=-sinh(z)+cosh(z)." }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "\321\344\345\353\340\345\354 \+
\361\356\356\362\342\345\362\361\362\342\363\376\371\350\345 \357\356
\344\361\362\340\355\356\342\352\350" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 139 "WS:=subs(exp(1/2*Pi*n/q*y)=sinh(1/2*Pi*n/q*y)+cosh(1
/2*Pi*n/q*y),exp(-1/2*Pi*n/q*y)=-sinh(1/2*Pi*n/q*y)+cosh(1/2*Pi*n/q*y)
,R=Pi*n*b/q,Ws): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "WS:=si
mplify(WS): WS;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*&%#QnG\"\"\"-%
%sinhG6#,$*,\"\"#!\"\"%#PiGF'%\"nGF'%\"qGF.%\"yGF'F'F'F'*(%#CnGF'-F)6#
**F/F'F0F'F1F.%\"bGF'F'-%%coshGF*F'F'*(F4F'-F:F6F'F(F'F.F'F5F." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "\317\356\361\353\345 \344\345\353
\345\355\350\377 \355\340 sinh(Pi*n/q*b) \357\356\353\363\367\350\354 \+
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "WSu:=y->Cn*cosh(1/2*Pi*
n/q*y)+(Qn/sinh(Pi*n/q*b)-Cn*coth(Pi*n/q*b))*sinh(1/2*Pi*n/q*y);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$WSuGf*6#%\"yG6\"6$%)operatorG%&arro
wGF(,&*&%#CnG\"\"\"-%%coshG6#,$*&#F/\"\"#F/**%#PiGF/%\"nGF/%\"qG!\"\"9
$F/F/F/F/F/*&,&*&%#QnGF/-%%sinhG6#**F8F/F9F/F:F;%\"bGF/F;F/*&F.F/-%%co
thGFCF/F;F/-FBF2F/F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
58 "WnS:=(x,y)->sum(WSu(y)*sin(Pi*n/2/q*x), n=1..N); WnS(x,y);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$WnSGf*6$%\"xG%\"yG6\"6$%)operatorG%
&arrowGF)-%$sumG6$*&-%$WSuG6#9%\"\"\"-%$sinG6#,$*&#F5\"\"#F5**%#PiGF5%
\"nGF5%\"qG!\"\"9$F5F5F5F5/F?;F5%\"NGF)F)F)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$sumG6$*&,&*&%#CnG\"\"\"-%%coshG6#,$*,\"\"#!\"\"%#PiG
F*%\"nGF*%\"qGF1%\"yGF*F*F*F**&,&*&%#QnGF*-%%sinhG6#**F2F*F3F*F4F1%\"b
GF*F1F**&F)F*-%%cothGF<F*F1F*-F;F-F*F*F*-%$sinG6#,$*,F0F1F2F*F3F*F4F1%
\"xGF*F*F*/F3;F*%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "WnS(0,0);WnS(q,0); " }{TEXT -1 10 "- \357\360\356\342\345\360\352
\340" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$sumG6$*&%#CnG\"\"\"-%$sinG6#,$*(\"\"#!\"\"%#PiGF(%\"
nGF(F(F(/F1;F(%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "\310
\361\357\356\353\374\347\363\377 \342\373\370\345 \357\360\350\342\345
\344\345\355\355\373\345 \364\356\360\354\363\353\373, \343\360\340
\364\350\352\350 \357\356\361\362\360\356\350\362\374 \355\345 \363
\344\340\345\362\361\377!? \317\356\367\345\354\363, \357\356\355\377
\362\374" }}{PARA 0 "" 0 "" {TEXT -1 97 "\355\345 \354\356\343\363!  -
----------------------------------------------------------------------
----------------" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "\317\360\356
\342\345\344\345\354 \356\357\360\345\344\345\353\345\355\350\345 Cn \+
\350  Qn" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Cn:=C(n): Qn:=Q
(n):Cn;Qn;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\"\"#\"\"\"%\"qGF%%
\"GGF&,&F%F&*&)!\"\"%\"nGF&,&*&)%#PiGF%F&)F-F%F&F&F%F,F&F&F&F1!\"$F-F3
F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*.\"\"#\"\"\"%\"qGF%%\"GGF&,&F
%F&*&)!\"\"%\"nGF&,&*&)%#PiGF%F&)F-F%F&F&F%F,F&F&F&F1!\"$F-F3F&*.F%F&F
(F&%\"bGF%,&F+F&F&F,F&F1F,F-F,F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
21 "\300\355\340\353\356\343\350\367\355\356 \344\353\377 V(x,y)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Cvn:=Cv(n): Cvn; Qvn:=Qv(n):
 Qvn;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.\"\"#\"\"\"%\"bGF%%\"GGF&
,*F%F&*&F%F&-%$cosG6#*&%#PiGF&%\"nGF&F&!\"\"*()F/F%F&)F0F%F&F+F&F&**F%
F&F/F&F0F&-%$sinGF-F&F1F&F/!\"$F0F8F&" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&*.\"\"#\"\"\"%\"bGF%%\"GGF&,&F%F&*&)!\"\"%\"nGF&,&*&)%#PiGF%F&)F-
F%F&F&F%F,F&F&F&F1!\"$F-F3F&*.F%F&F(F&%\"qGF%,&F+F&F&F,F&F1F,F-F,F&" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "\323\352\340\346\345\354  \347
\344\345\361\374 \361\356\356\362\342\345\362\361\362\342\350\345 (q ~
 a) \354\345\346\344\363:   Cn = 2*\303[1,n](q);    Qn = 2*\303[2,n](q
,b);" }}{PARA 0 "" 0 "" {TEXT -1 115 "                                \+
                                           Cvn = 2*\303[1,n](b);  Qvn \+
= 2*\303[2,n](b,q);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 51 "\307\340\357\350\370\345\354  \361\363\354\354
\363 Wn(x,y) \361 \356\343\360\340\355\350\367\345\355\355\373\354 \+
\367\350\361\353\356\354 \367\353\345\355\356\342" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 85 "NN:=70:Wn:=(x,y)->sum((Ah*exp(r(n)*y)+Bh*exp
(-r(n)*y))*sin(r(n)*x), n=1..NN);Wn(x,y):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#WnGf*6$%\"xG%\"
yG6\"6$%)operatorG%&arrowGF)-%$sumG6$*&,&*&%#AhG\"\"\"-%$expG6#*&-%\"r
G6#%\"nGF49%F4F4F4*&%#BhGF4-F66#,$F8!\"\"F4F4F4-%$sinG6#*&F9F49$F4F4/F
<;F4%#NNGF)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "\300\355\340
\353\356\343\350\367\355\356 \344\353\377 V(x,y)" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 84 "Vn:=(x,y)->sum((Avh*exp(ry(n)*x)+Bvh*exp(-ry(
n)*x))*sin(ry(n)*y), n=1..NN); Vn(x,y):" }{TEXT -1 0 "" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#VnGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)-%$s
umG6$*&,&*&%$AvhG\"\"\"-%$expG6#*&-%#ryG6#%\"nGF49$F4F4F4*&%$BvhGF4-F6
6#,$F8!\"\"F4F4F4-%$sinG6#*&F9F49%F4F4/F<;F4%#NNGF)F)F)" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 329 17 "\307\340\344\340\344\350\354 \357\340
\360\340\354\345\362\360\373" }{TEXT 334 1 "." }{TEXT -1 59 "   (L=2*q
; Ly=2*b) . \317\360\350\354\345\367\340\355\350\345: \344\353\377 q>1
 \355\345 \361\362\360\356\350\362 \343\360\340\364\350\352!?" }}
{PARA 0 "" 0 "" {TEXT -1 108 "___________-----------------------------
-----------------------______________________-----------------------" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "G:=-1:q:=1:b:=1: " }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "\316\341\377\347\340\362\345\353
\374\355\356 \356\357\360\345\344\345\353\350\362\374 \357\340\360\340
\354\345\362\360\373 R \350 Rv \350\355\340\367\345 \357\345\367\340
\362\374 \355\345 \341\363\344\345\362 \360\340\341\356\362\340\362
\374!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "R:=Pi*n/L*Ly; r(n)
; Rv:=Pi*n/Ly*L; ry(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG*&%#P
iG\"\"\"%\"nGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#!\"\"%#PiG
\"\"\"%\"nGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#RvG*&%#PiG\"\"\"
%\"nGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#!\"\"%#PiG\"\"\"%
\"nGF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 79 "\310\362\340\352, \+
\350\354\345\345\354 \352\356\354\357\356\355\345\355\362\373 w(x,y) \+
\350 v(x,y) \360\345\370\345\355\350\377 \344\350\364\364\345\360\345
\355\366\350\340\353\374\355\356\343\356 \363\360\340\342\355\345\355
\350\377 (3) " }}{PARA 0 "" 0 "" {TEXT 330 7 "\342  \342\350\344\345" 
}{TEXT -1 24 " (13) - Wn  \350 (14) - Vn:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 42 "\317\356\361\362\360\356\350\354 \343\360\340\364\350\352
, \344\353\377 \347\340\344\340\355\355\373\365 \357\340\360\340\354
\345\362\360\356\342: " }}{PARA 0 "" 0 "" {TEXT -1 84 "R = Pi*n/L*Ly =
 r(n)*Ly;  L:=2*q, Ly:=2*b, (q \350 b \354\356\343\363\362 \341\373
\362\374 \360\340\342\355\373\354\350); r(n)=Pi*n/L: " }}{PARA 0 "" 0 
"" {TEXT -1 91 "ry(n)=Pi*n/Ly: N:=infinity:  0<x<L,  0<y<Ly; G; Cn=C(n
), Qn=Q(n); Rv = Pi*n/Ly*L = ry(n)*L;" }}{PARA 0 "" 0 "" {TEXT -1 21 "
Cvn=Cv(n), Qvn=Qv(n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " e
valf(Wn(1,1));evalf(Vn(1,1)); " }{TEXT -1 2 "- " }{TEXT 328 17 "\352
\356\355\362\360\356\353\374\355\340\377 \362\356\367\352\340" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+pqUtR!#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+pqUtR!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "
\307\340\344\340\355\350\345 \355\340 \357\356\361\362\360\356\345\355
\350\345 \343\360\340\364\350\352\350" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 65 "plot3d(Wn(x,y), x=0..L, y=0..Ly,axes=boxed,orientatio
n=[-53,46]);" }}{PARA 13 "" 1 "" {GLPLOT3D 270 235 235 {PLOTDATA 3 "6&
-%%GRIDG6%;$\"\"!F($\"\"#F(F&X0%)anythingG6\"6\"[gl'!%\"!!#\\bm\":\":!
!!!0000000000000000000000000000000000000000000000000000000000000000000
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