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\363\361\353\356\342 \350\351, \352\356\362\356\360\373\345 \341\363\344\363\362 \356\357 \360\345\344\345\353\377\362\374" }}{PARA 0 "" 0 "" {TEXT -1 46 "(\347 \340\344\340\367\340 \330\362\363\360\354\340-\313\350\363\342\350\353 \353\377) \361\356\341\361\362\342\345\355\355\373\345 \347\355\340 \367\345\355\350\377 " }{TEXT 547 1 "b" }{TEXT -1 1 "(" }{TEXT 548 1 " n" }{TEXT -1 24 ") \350 \361\356\341\361\362\342\345\355\355\373\345 \+ \364\363\355\352\366\350\350 " }{TEXT 549 2 "Xn" }{TEXT -1 1 "(" } {TEXT 550 1 "x" }{TEXT -1 1 "," }{TEXT 551 1 "n" }{TEXT -1 3 "), " }} {PARA 0 "" 0 "" {TEXT -1 74 "\340 \362\340\352\346\345 \357\356\344 \341\350\360\340\345\354\363\376 \342 \363\352\340\347\340\355\355\356 \354 \342\373\370\345 \361\354\373\361\353\345 \352 \343\360\340\355 \350\367\355\373\354 \363\361\353\356\342\350\377\354 \364\363\355 \352\366\350\376 " }{TEXT 552 1 "z" }{TEXT -1 1 "(" }{TEXT 553 1 "x" } {TEXT -1 1 "," }{TEXT 554 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 38 "if u(0,t)=phi(t)and u(L,t)=psi(t) then" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "b:=n->Pi*n/L: Xn:=(x,n)->sin(b(n)*x ):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->phi(t)+x/L*(psi(t)-ph i(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arrowG6\",&-%$phiG6#F( \"\"\"*(F'F2%\"LG!\"\",&-%$psiG6#F(F2-F06#F(F5F2F2F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "elif D[1](u)(0,t)=phi(t) and D[1](u)(L,t)=psi (t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "b:=n->Pi*n/L: Xn:=(x,n) ->cos(b(n)*x): " }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->x*phi(t) +x^2/2/L*(psi(t)-phi(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arr owG6\",&*&F'\"\"\"-%$phiG6#F(F0F0**F'\"\"#F5!\"\"%\"LGF6,&-%$psiG6#F(F 0-F26#F(F6F0F0F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "elif D[1](u )(0,t)=phi(t) and u(L,t)=psi(t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "b:=n->Pi*(2*n-1)/2/L: Xn:=(x,n)->cos(b(n)*x):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->x*phi(t)+(psi(t)-L*phi(t))" "6#>%\"zGf*6$% \"xG%\"tG7\"6$%)operatorG%&arrowG6\",&*&F'\"\"\"-%$phiG6#F(F0F0,&-%$ps iG6#F(F0*&%\"LGF0-F26#F(F0!\"\"F0F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "elif u(0,t)=phi(t) and D[1](u)(L,t)=psi(t) then" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 45 "b:=n->Pi*(2*n-1)/2/L: Xn:=(x,n)->sin(b(n)*x): " }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->phi(t)+x*psi(t)" "6#>% \"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arrowG6\",&-%$phiG6#F(\"\"\"*&F'F2 -%$psiG6#F(F2F2F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "\317\360\356\342\345\344\345\354 \+ \342\350\347\363\340\353\350\347\340\366\350\376 \342\373\341\360\340 \355\355\373\365 \361\356\341\361\362\342\345\355\355\373\365 \347\355 \340\367\345\355\350\351 " }{TEXT 564 1 "b" }{TEXT -1 1 "(" }{TEXT 565 1 "n" }{TEXT -1 23 "), \361\356\341\361\362\342\345\355\355\373 \365 \364\363\355\352\366\350\351 " }}{PARA 0 "" 0 "" {TEXT 566 2 "Xn " }{TEXT -1 1 "(" }{TEXT 567 1 "x" }{TEXT -1 1 "," }{TEXT 568 1 "n" } {TEXT -1 12 ") \350 \364\363\355\352\366\350\350 " }{TEXT 569 1 "z" } {TEXT -1 1 "(" }{TEXT 570 1 "x" }{TEXT -1 1 "," }{TEXT 571 1 "t" } {TEXT -1 2 ")." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "b(n);Xn(x ,n); z(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%#PiG\"\"\"%\"nGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#*(%#PiG\"\"\"%\"nGF(%\"xGF( " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"\"F$*&%\"xGF$,&-%%coshG6#F$F $F$!\"\"F$F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "\317\360\356\342 \345\360\350\354 \355\340 \356\344\355\356\360\356\344\355\356\361\362 \374 \357\356\353\363\367\345\355\355\373\365 \343\360\340\355\350\367 \355\373\365 \363\361\353\356\342\350\351 \344\353\377 \342\342\356 \344\350\354\356\351 \342 \357\356\361\353\345\344\363\376\371\345\354 " }}{PARA 0 "" 0 "" {TEXT -1 61 "\364\363\355\352\366\350\350 W(x,t), \342\373\341\360\340\342 \355\350\346\345 \355\363\346\355\363\376 \+ \361\362\360\356\367\352\363 \350 \361\355\377\342 \340\357\356\361 \362\360\356\364\373. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "W w(x,t): Ww(0,t)=u(0,t)-z(0,t); Ww(L,t)=u(L,t)-z(L,t); " }{TEXT -1 2 "1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"!%\"tGF'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"\"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "D[1](Ww)(0,t)=D[1](u)(0,t)-D[1](z)( 0,t); D[1](Ww)(L,t)=D[1](u)(L,t)-D[1](z)(L,t); " }{TEXT -1 2 "2)" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$\"\"!%\"tG,( --F&6#%\"uGF,F)-%%coshGF(!\"\"F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# /--&%\"DG6#\"\"\"6#%#WwG6$F)%\"tG,(--F&6#%\"uGF,F)-%%coshGF(!\"\"F)F) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "D[1](Ww)(0,t)=D[1](u)(0 ,t)-D[1](z)(0,t); Ww(L,t)=u(L,t)-z(L,t); " }{TEXT -1 2 "3)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$\"\"!%\"tG,(--F&6# %\"uGF,F)-%%coshGF(!\"\"F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#Ww G6$\"\"\"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "Ww(0 ,t)=u(0,t)-z(0,t); D[1](Ww)(L,t)=D[1](u)(L,t)-D[1](z)(L,t); " }{TEXT -1 2 "4)" }{MPLTEXT 1 0 3 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%# WwG6$\"\"!%\"tGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\" 6#%#WwG6$F)%\"tG,(--F&6#%\"uGF,F)-%%coshGF(!\"\"F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 324 12 "\317\360\350\354\345\367\340\355\350\345. " } {TEXT -1 67 "\307\340\357\350\370\345\354 \344\353\377 1-\351 \352\360 \340\345\342\356\351 \347\340\344\340\367\350 \362\340\352 \355\340 \347\373\342\340\345\354\373\345 \363\361\353\356\342\350\377 \361\356 \343\353\340\361\356\342\340\355\350\377:" }{TEXT 331 1 " " }}{PARA 0 "" 0 "" {TEXT 572 1 "u" }{TEXT -1 6 "(0,0)=" }{TEXT 325 1 "f" }{TEXT -1 4 "(0)=" }{TEXT 326 3 "phi" }{TEXT -1 6 "(0) \350 " }{TEXT 327 1 "u " }{TEXT -1 1 "(" }{TEXT 330 1 "L" }{TEXT -1 4 ",0)=" }{TEXT 328 1 "f " }{TEXT -1 1 "(" }{TEXT 332 1 "L" }{TEXT -1 2 ")=" }{TEXT 329 3 "psi " }{TEXT -1 53 "(0), \342\373\357\356\353\355\345\355\350\345 \352\356 \362\356\360\373\365 \355\345\353\374\347\377 \361\352\340\347\340\362 \374 \356\341\377\347\340\362\345\353\374\355\356\345, " }}{PARA 0 "" 0 "" {TEXT -1 76 "\355\356 - \346\345\353\340\362\345\353\374\355\356 \345. \310\347\354\345\355\345\355\350\345 \343\360\340\355\350\367 \355\373\365 \363\361\353\356\342\350\351 \350\347\354\345\355\377\345 \362 \363\361\353\356\342\350\377 \361\356\343\353\340\361\356\342\340 \355\350\377." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "if f(0)=ph i(0) and f(L)=psi(0) then sogL:=`\363\361\353\356\342\350\377 \361\356 \343\353\340\361\356\342\340\355\350\377 \342\373\357\356\353\355\345 \355\373` " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "else sogL:=`\363\361 \353\356\342\350\377 \361\356\343\353\340\361\356\342\340\355\350\377 \+ \355\345 \342\373\357\356\353\355\345\355\373` fi: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "\350 \357\360\350\342\345\344\345\354 \342\350 \347\363\340\353\350\347\340\366\350\376 \350\365 \342\373\357\356\353 \355\345\355\350\377 \355\340 \344\350\361\357\353\345\345" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "sogL; " }{TEXT -1 6 "\316\362\342 \345\362:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?|^z|\\z|fy|iy|]y|cy|jz~ |\\z|iy|^y|fy|[y|\\z|iy|]y|[y|hy|cy|jz~|]y|fz|jy|iy|fy|hy|`y|hy|fzG" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "*) \307\340\344\340\344\350\354 \+ \352\356\355\352\360\345\362\355\363\376 \364\363\355\352\366\350\376 \+ \342\356\347\354\363\371\345\355\350\377, \355\340\357\360\350\354\345 \360:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "g:=(x,t)->-cosh(x) +sinh(x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6$%\"xG%\"tG6\"6 $%)operatorG%&arrowGF),&-%%coshG6#9$!\"\"-%%sinhGF0\"\"\"F)F)F)" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "\317\360\350 \375\362\356\354 0<" }{TEXT 284 1 "x" }{TEXT -1 1 "<" }{TEXT 285 1 "L" }{TEXT -1 2 ", " } {TEXT 286 2 " t" }{TEXT -1 66 ">0, \367\362\356 \342\356 \354\355\356 \343\356\354 \356\341\363\361\353\356\342\353\345\355\356 \357\360\345 \344\361\362\340\342\353\345\355\350\345\354 \360\345\370\345\355\350 \377 \342 \342\350\344\345 \360\377\344\340. " }}{PARA 0 "" 0 "" {TEXT -1 80 "\304\340\353\345\345 \357\356\361\362\360\356\345\355\350 \345 \360\345\370\345\355\350\377 \350\344\345\362 \342 \340\342\362 \356\354\340\362\350\367\345\361\352\356\354 \360\345\346\350\354\345 \+ \342 \361\356\356\362\342\345\362\361\362\342\350\350 \361 \354\345 \362\356\344\350\352\356\351" }}{PARA 0 "" 0 "" {TEXT -1 82 "\345\343 \356 \352\356\354\357\374\376\362\345\360\355\356\343\356 \350\347\353 \356\346\345\355\350\377 \350 \357\356\347\342\356\353\377\345\362 \+ \342\345\361\362\350 \344\345\362\340\353\374\355\373\351 \340\355\340 \353\350\347, \342 \362\356\354 \367\350\361\353\345 \343\360\340\364 \350-" }}{PARA 0 "" 0 "" {TEXT -1 42 "\367\345\361\352\350\351, \352 \340\346\344\356\343\356 \357\360\356\354\345\346\363\362\356\367\355 \356\343\356 \360\345\347\363\353\374\362\340\362\340." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "\320\345\370\345\355\350\345 \350\361\365 \356\344\355\356\343\356 \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, \363 \344\356\342\353\345\362\342\356\360\377\376\371\345\343\356 \342\373 \370\345 \361\364\356\360\354\363\353\350-" }}{PARA 0 "" 0 "" {TEXT -1 65 "\360\356\342\340\355\355\373\354 \352\360\340\345\342\373\354 \+ \363\361\353\356\342\350\377\354, \352\340\352 \341\373\353\356 \361 \352\340\347\340\355\356, \341\363\344\345\354 \350\361\352\340\362 \374 \342 \342\350\344\345 " }}{PARA 0 "" 0 "" {TEXT 440 1 "u" }{TEXT -1 1 "(" }{TEXT 441 1 "x" }{TEXT -1 1 "," }{TEXT 442 1 "t" }{TEXT -1 2 ")=" }{TEXT 443 1 "z" }{TEXT -1 1 "(" }{TEXT 444 1 "x" }{TEXT -1 1 " ," }{TEXT 445 1 "t" }{TEXT -1 2 ")+" }{TEXT 451 1 "w" }{TEXT -1 1 "(" }{TEXT 446 1 "x" }{TEXT -1 1 "," }{TEXT 447 1 "t" }{TEXT -1 2 ")+" } {TEXT 448 1 "v" }{TEXT -1 1 "(" }{TEXT 449 1 "x" }{TEXT -1 1 "," } {TEXT 450 1 "t" }{TEXT -1 26 ") \350 \355\340\365\356\344\350\362\374 \+ \350\347 \363\360\340\342\355\345\355\350\377:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {XPPEDIT 19 1 "de:=a^2*diff(u(x,t),x$2)-diff(u(x,t),t$2)+g(x,t) =0:" "6#>%#deG/,(*&%\"aG\"\"#-%%diffG6$-%\"uG6$%\"xG%\"tG-%\"$G6$F0F) \"\"\"F5-F+6$-F.6$F0F1-F36$F1F)!\"\"-%\"gG6$F0F1F5\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "\304\353\377 \352\340\346\344\356\351 \+ \352\356\354\357\356\355\345\355\362\373 \360\345\370\345\355\350\377 \+ " }{TEXT 467 1 "u" }{TEXT -1 1 "(" }{TEXT 468 1 "x" }{TEXT -1 1 "," } {TEXT 469 1 "t" }{TEXT -1 9 "), \352\360\356\354\345 " }{TEXT 573 1 "z " }{TEXT -1 1 "(" }{TEXT 574 1 "x" }{TEXT -1 1 "," }{TEXT 575 1 "t" } {TEXT -1 33 "), \347\340\357\350\370\345\354 \361\342\356\270 \344\350 \364\364\345\360\345\355\366\350\340\353\374\355\356\345 " }}{PARA 0 " " 0 "" {TEXT -1 82 "\363\360\340\342\355\345\355\350\345 \361 \367\340 \361\362\355\373\354\350 \357\360\356\350\347\342\356\344\355\373\354 \350, \350\347 \352\356\362\356\360\356\343\356 \356\355\340 \344\356 \353\346\355\340 \356\357\360\345\344\345\353\377\362\374\361\377, \+ \342 \363\344\356\341\355\356\354 " }}{PARA 0 "" 0 "" {TEXT -1 50 " \344\353\377 \344\340\353\374\355\345\351\370\350\365 \342\373\367\350 \361\353\345\355\350\351 \342\350\344\345. \316\344\355\340 \350\347 \+ \352\356\354\357\356\355\345\355\362 " }{TEXT 428 1 "z" }{TEXT -1 1 "( " }{TEXT 429 1 "x" }{TEXT -1 1 "," }{TEXT 430 1 "t" }{TEXT -1 10 ") \+ \360\345\370\345\355\350\377 " }{TEXT 431 1 "u" }{TEXT -1 1 "(" } {TEXT 432 1 "x" }{TEXT -1 1 "," }{TEXT 433 1 "t" }{TEXT -1 15 ") \363 \346\345 \350\347\342\345\361\362\355\340 " }}{PARA 0 "" 0 "" {TEXT -1 81 "\350 \345\270 \347\340\357\350\361\374 \357\360\350\342\356\344 \350\362\361\377 \355\350\346\345. \304\342\345 \344\360\363\343\350 \345 \341\363\344\345\354 \350\361\352\340\362\374 \350\347 \357\360 \350\342\356\344\350\354\373\365 \355\350\346\345 \344\350\364\364\345 \360\345\355-" }}{PARA 0 "" 0 "" {TEXT -1 31 "\366\350\340\353\374\355 \373\365 \363\360\340\342\355\345\355\350\351. \312\356\354\357\356 \355\345\355\362\363 " }{TEXT 439 1 "w" }{TEXT -1 1 "(" 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\302\373\367\350\361\353\350\354 \352\356\375\364 \364\350\366\350\345\355\362\373 \360\377\344\340 \324\363\360\374\345 :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "- \352\356\375\364\364\350 \366\350\345\355\362 \360\377\344\340 \324\363\360\374\345 \364\363 \355\352\366\350\350, \347\340\344\340\376\371\345\351 \342\356\347 \354\363\371\345\355\350\345, \354\356\346\345\362 \341\373\362\374 \+ \357\360\345\344\361\362\340\342\353\345\355 \342 " }}{PARA 0 "" 0 "" {TEXT -1 5 "\342\350\344\345:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "q:=(n,t)->2/L*int(g1(x,t)*Xn(x,n), x=0..L): q(n,t):=subs(cos(Pi* n)=(-1)^n,sin(Pi*n)=0,q(n,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-% \"qG6$%\"nG%\"tG,$*(\"\"#\"\"\",&*&%#PiGF,F'F,!\"\"**-%$expG6#F0F,F/F, F'F,)F0F'F,F,F,,&F,F,*&)F/F+F,)F'F+F,F,F0F," }}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 0 "" }{TEXT 391 26 "\317\360\356\342\345\360\352\340 (\354 \356\346\355\356 \356\357\363\361\362\350\362\374)." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 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"6#>-%\"GG6$%\"nG%\"tG,$*,\"\"#\"\"\"%#Pi GF,F'F,,&F,!\"\"*&-%$expG6#F/F,)F/F'F,F,F,,&F,F,*&)F-F+F,)F'F+F,F,F/F, " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "\304\360\363\343\356\351 - \+ " }{TEXT 404 2 "zg" }{TEXT -1 1 "(" }{TEXT 405 1 "n" }{TEXT -1 1 "," } {TEXT 406 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "zg:=(n,t)->-2/L*int(D[2,2](z)(x,t)*Xn(x,n), x=0..L): zg(n,t);" " 6#C$>%#zgGf*6$%\"nG%\"tG7\"6$%)operatorG%&arrowG6\",$*(\"\"#\"\"\"%\"L G!\"\"-%$intG6$*&--&%\"DG6$F1F16#%\"zG6$%\"xGF)F2-%#XnG6$FAF(F2/FA;\" \"!F3F2F4F.F.F.-F%6$F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "\307\340\357\350\370\345\354 \344 \353\377 \357\360\356\342\345\360\352\350 \357\356\353\363\367\345\355 \355\373\351 \342\373\370\345 \360\345\347\363\353\374\362\340\362, \+ \355\356 \357\356\344 \344\360\363\343\350\354 \350\354\345\355\345 \354 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "gg:=(n,t)->G(n,t)+ zg(n,t):gg(n,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#\"\"\"%#P iGF&%\"nGF&,&F&!\"\"*&-%$expG6#F*F&)F*F(F&F&F&,&F&F&*&)F'F%F&)F(F%F&F& F*F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "\317\360\350" }{TEXT 413 1 " " }{TEXT -1 24 "\375\362\356\354 \344\356\353\346\355\356 \342\373 \357\356\353\355\377\362\374\361\377:" }{TEXT 407 3 " q" }{TEXT -1 1 "(" }{TEXT 408 1 "n" }{TEXT -1 1 "," }{TEXT 409 1 "t" }{TEXT -1 2 ")= " }{TEXT 410 2 "gg" }{TEXT -1 1 "(" }{TEXT 411 1 "n" }{TEXT -1 1 "," } {TEXT 412 1 "t" }{TEXT -1 29 ") \350 \375\362\356 \354\356\346\345\362 \341\373\362\374 \357\360\356\342\345\360\352\356\351." }}{PARA 0 "" 0 "" {TEXT -1 24 "\317\360\356\342\345\360\352\340 \357\360\356\370 \353\340 \363\361\357\345\370\355\356." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "3.2. \310, \355\340\352\356 \355\345\366, \347\340\357\350\370\345\354 \361\340\354\363 3-\376 \+ \352\356\354\357\356\355\345\355\362\363 " }{TEXT 366 1 "v" }{TEXT -1 1 "(" }{TEXT 367 1 "x" }{TEXT -1 1 "," }{TEXT 368 1 "t" }{TEXT -1 2 ") :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "v:=(x,t)->sum((int(q( n,tau)*sin(b(n)*a*(t-tau)), tau=0..t)*Xn(x,n)/(b(n)*a)), n=1..N): v(x, t):=simplify(v(x,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"vG6$%\"x G%\"tG-%$sumG6$,$*.\"\"#\"\"\"%#PiG!\"\"%\"nGF1,*-%$cosG6#*(F0F/F2F/F( F/F1*(F4F/-%$expG6#F1F/)F1F2F/F/F/F/*&F9F/F " 0 "" {MPLTEXT 1 0 7 "v(0,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 315 51 "4. \310\362\340\352, \350\354\345\345 \354 \360\345\370\345\355\350\345 \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 \+ " }{TEXT 314 2 "de" }{TEXT 316 21 " \342 \356\352\356\355\367\340\362 \345\353\374\355\356\354 \342\350\344\345" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "`U:=(x,t)->z(x,t)+W(x,t)+v(x,t)`: ` U(x,t):=simplify(U(x,t))`:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "U:=(x,t)->1+x*(cosh(1)-1)+sum((-1)^n*(2*(-1)^(1+n)+exp(1)+1/exp(1 ))/Pi/n/(1+Pi^2*n^2)*cos(Pi*n*t)*sin(Pi*n*x),n = 1 .. N)+sum(-2/Pi/n*( -cos(Pi*n*t)+cos(Pi*n*t)*exp(-1)*(-1)^n+1-exp(-1)*(-1)^n)*sin(Pi*n*x)/ (1+Pi^2*n^2),n = 1 .. N);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"UGf*6 $%\"xG%\"tG6\"6$%)operatorG%&arrowGF),*\"\"\"F.*&9$F.,&-%%coshG6#F.F.F .!\"\"F.F.-%$sumG6$*0)F5%\"nGF.,(*&\"\"#F.)F5,&F.F.F;F.F.F.-%$expGF4F. *&F.F.FAF5F.F.%#PiGF5F;F5,&F.F.*&)FDF>F.)F;F>F.F.F5-%$cosG6#*(FDF.F;F. 9%F.F.-%$sinG6#*(FDF.F;F.F0F.F./F;;F.%\"NGF.-F76$,$*.F>F.FDF5F;F5,*FIF 5*(FIF.-FB6#F5F.F:F.F.F.F.*&FenF.F:F.F5F.FNF.FEF5F5FRF.F)F)F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "NN:=10: " }{TEXT -1 47 "- \+ \344\353\377 \363\354\345\355\374\370\345\355\350\377 \342\360\345\354 \345\355\350 \361\367\345\362\340 \350 \356\341\372\270\354\340 \357 \340\354\377\362\350." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "*) \327 \362\356\341\373 \347\340\357\350\361\340\362\374 " }{TEXT 596 2 "NN" }{TEXT -1 48 "-\376 \367\340\361\362\350\367\355\363\376 \361\363\354 \354\363 \357\360\356\342\345\344\345\354 \352\356\357\350\360\356\342 \340\355\350\345 \360\345\370\345\355\350\377." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "*) \302\342\345\344\345\354 \356\341\356\347\355\340 \367\345\355\350\345 " }{TEXT 417 2 "NN" }{TEXT -1 54 "-\351 \367\340 \361\362\350\367\355\356\351 \361\363\354\354\373 \357\356\353\363\367 \345\355\355\356\343\356 \360\345\370\345\355\350\377 \350 \347\340 \357\350\370\345\354 \345\343\356 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 233 "Un:=(x,t)->1+x*(cosh(1)-1)+sum((-1)^n*(2*(-1)^(1+n)+ exp(1)+1/exp(1))/Pi/n/(1+Pi^2*n^2)*cos(Pi*n*t)*sin(Pi*n*x),n = 1 .. NN )+sum(-2/Pi/n*(-cos(Pi*n*t)+cos(Pi*n*t)*exp(-1)*(-1)^n+1-exp(-1)*(-1)^ n)*sin(Pi*n*x)/(1+Pi^2*n^2),n = 1 .. NN);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#UnGf*6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF),*\"\"\"F .*&9$F.,&-%%coshG6#F.F.F.!\"\"F.F.-%$sumG6$*0)F5%\"nGF.,(*&\"\"#F.)F5, &F.F.F;F.F.F.-%$expGF4F.*&F.F.FAF5F.F.%#PiGF5F;F5,&F.F.*&)FDF>F.)F;F>F .F.F5-%$cosG6#*(FDF.F;F.9%F.F.-%$sinG6#*(FDF.F;F.F0F.F./F;;F.%#NNGF.-F 76$,$*.F>F.FDF5F;F5,*FIF5*(FIF.-FB6#F5F.F:F.F.F.F.*&FenF.F:F.F5F.FNF.F EF5F5FRF.F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "\307\340\354 \345\362\350\354, \367\362\356 \347\355\340\367\345\355\350\345 \375 \362\356\343\356 \357\360\345\344\345\353\340 limit(" }{TEXT 481 2 "U n" }{TEXT -1 1 "(" }{TEXT 482 1 "x" }{TEXT -1 1 "," }{TEXT 483 1 "t" } {TEXT -1 3 "), " }{TEXT 480 2 "NN" }{TEXT -1 11 "=infinity)=" }{TEXT 477 1 "U" }{TEXT -1 1 "(" }{TEXT 478 1 "x" }{TEXT -1 1 "," }{TEXT 479 1 "t" }{TEXT -1 16 ") \360\340\342\355\356 \364\363\355\352\366\350 \350 " }{TEXT 474 1 "U" }{TEXT -1 1 "(" }{TEXT 475 1 "x" }{TEXT -1 1 " ," }{TEXT 476 1 "t" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 317 11 "5. \317\360\356\342\345\360\352\340" }{TEXT -1 31 ". \317\356 \344\361\362\340\342\350\354 \357\356\353\363\367\345\355\355\356\345 \+ \360\345\370\345\355\350\345 " }{TEXT 414 1 "U" }{TEXT -1 1 "(" } {TEXT 415 1 "x" }{TEXT -1 1 "," }{TEXT 416 1 "t" }{TEXT -1 36 ") \342 \350\361\365\356\344\355\356\345 \344\350\364\364\345\360\345\355\366 \350\340\353\374\355\356\345 \363\360\340\342-" }}{PARA 0 "" 0 "" {TEXT -1 6 "\355\345\355\350\345 " }{TEXT 256 2 "de" }{TEXT -1 1 ":" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "re:=subs(u(x,t)=Un(x,t),de ): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 3 "5.1" }{TEXT -1 80 ". \302 \+ \357\360\340\342\350\353\374\355\356\361\362\350 \357\356\353\363\367 \345\355\355\356\343\356 \360\345\370\345\355\350\377 \354\356\346\355 \356 \363\341\345\344\350\362\374\361\377, \347\340\357\363\361\362 \350\342 \357\360\356\366\345\344\363\360\363 \363\357\360\356\371\345 -" }}{PARA 0 "" 0 "" {TEXT -1 82 "\355\350\377, \342 \360\345\347\363 \353\374\362\340\362\345 \352\356\362\356\360\356\351 \344\356\353\346 \355\373 \357\356\353\363\367\350\362\374 \362\356\346\344\345\361\362 \342\356 \350\353\350 \350\347-\347\340 \356\343\360\340\355\350\367 \345\355\355\356\343\356 \367\350\361\353\340 " }}{PARA 0 "" 0 "" {TEXT -1 45 "\367\353\345\355\356\342 \360\377\344\340 \362\356\353 \374\352\356 \357\360\350\341\353\350\347\350\362\345\353\374\355\356 \345 \362\356\346\344\345\361\362\342\356." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "simplify(re):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "\317\356\353\363\367\345\355\355\356\345 \362\356\346\344\345\361 \362\342\356 (\345\343\356 \353\345\342\363\376 \367\340\361\362\374) \+ \357\360\356\350\353\353\376\361\362\360\350\360\363\345\354 \343\360 \340\364\350\367\345\361\352\350. \304\353\377 \375\362\356\343\356 \+ \360\340\361-" }}{PARA 0 "" 0 "" {TEXT -1 16 "\361\354\356\362\360\350 \354 \364\363\355\352\366\350\376 " }{TEXT 418 2 "Un" }{TEXT -1 1 "(" }{TEXT 419 1 "x" }{TEXT -1 1 "," }{TEXT 420 1 "t" }{TEXT -1 34 ") \361 \356\343\360\340\355\350\367\345\355\355\373\354 \367\350\361\353\356 \354 \361\353\340\343\340\345\354\373\365." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "ren:=subs(u(x,t)=Un(x,t),de):" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 33 "\302 \360\345\347\363\353\374\362\340\362\345 \357 \356\353\363\367\350\354 \357\356\342\345\360\365\355\356\361\362\374 \+ " }{TEXT 484 3 "lhs" }{TEXT -1 1 "(" }{TEXT 485 3 "ren" }{TEXT -1 32 " ), \352\356\362\356\360\363\376 \357\360\345\344\361\362\340\342\350 \354 \343\360\340\364\350\367\345\361\352\350" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "plot3d(lhs(ren), x=0..L, t=0..6,axes=boxed,orien tation=[-33,56]);" }}{PARA 13 "" 1 "" {GLPLOT3D 494 191 191 {PLOTDATA 3 "6&-%%GRIDG6%;$\"\"!F($\"\"\"F(;F'$\"\"'F(X,%)anythingG6\"6\"[gl'!% \"!!#\\bm\":\":BFF0000000000000BFF0000000000000BFF0000000000000BFF0000 000000000BFF0000000000000BFF0000000000000BFF0000000000000BFF0000000000 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