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\364\363\355\352\366\350 \350 " }{TEXT 551 2 "Xn" }{TEXT -1 1 "(" }{TEXT 552 1 "x" }{TEXT -1 1 "," }{TEXT 553 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 554 1 "z" }{TEXT -1 1 "(" }{TEXT 555 1 "x" }{TEXT -1 1 "," }{TEXT 556 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)-phi(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$% )operatorG%&arrowG6\",&-%$phiG6#F(\"\"\"*(F'F2%\"LG!\"\",&-%$psiG6#F(F 2-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%&arrowG6\",&*&F'\"\"\"-%$phiG6#F(F 0F0**F'\"\"#F5!\"\"%\"LGF6,&-%$psiG6#F(F0-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*p hi(t)+(psi(t)-L*phi(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arro wG6\",&*&F'\"\"\"-%$phiG6#F(F0F0,&-%$psiG6#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->P i*(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$%\"xG%\"tG7\"6$%)operato rG%&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 566 1 "b" }{TEXT -1 1 "(" }{TEXT 567 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 568 2 "Xn" }{TEXT -1 1 "(" }{TEXT 569 1 "x" }{TEXT -1 1 "," }{TEXT 570 1 "n" }{TEXT -1 12 ") \350 \364\363\355\352 \366\350\350 " }{TEXT 571 1 "z" }{TEXT -1 1 "(" }{TEXT 572 1 "x" } {TEXT -1 1 "," }{TEXT 573 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 #-%$sinG6#*(%#PiG\"\"\"%\"nGF(%\"xGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "\317\360\356\342\345 \360\350\354 \355\340 \356\344\355\356\360\356\344\355\356\361\362\374 \357\356\353\363\367\345\355\355\373\365 \343\360\340\355\350\367\355 \373\365 \363\361\353\356\342\350\351 \344\353\377 \342\342\356\344 \350\354\356\351 \342 \357\356\361\353\345\344\363\376\371\345\354 " } }{PARA 0 "" 0 "" {TEXT -1 61 "\364\363\355\352\366\350\350 W(x,t), \+ \342\373\341\360\340\342 \355\350\346\345 \355\363\346\355\363\376 \+ \361\362\360\356\367\352\363 \350 \361\355\377\342 \340\357\356\361 \362\360\356\364\373. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "W w(x,t): Ww(0,t)=u(0,t)-z(0,t); Ww(L,t)=u(L,t)-z(L,t); " }{TEXT -1 2 "1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"!%\"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," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#Ww G6$F)%\"tG--F&6#%\"uGF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 " D[1](Ww)(0,t)=D[1](u)(0,t)-D[1](z)(0,t); Ww(L,t)=u(L,t)-z(L,t); " } {TEXT -1 2 "3)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#% #WwG6$\"\"!%\"tG--F&6#%\"uGF," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#W wG6$\"\"\"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "Ww( 0,t)=u(0,t)-z(0,t); D[1](Ww)(L,t)=D[1](u)(L,t)-D[1](z)(L,t); " }{TEXT -1 2 "4)" }{MPLTEXT 1 0 3 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%# WwG6$\"\"!%\"tGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\" 6#%#WwG6$F)%\"tG--F&6#%\"uGF," }}}{EXCHG {PARA 0 "" 0 "" {TEXT 325 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 332 1 " " }}{PARA 0 "" 0 "" {TEXT 574 1 "u" }{TEXT -1 6 "(0,0)=" }{TEXT 326 1 "f" }{TEXT -1 4 "(0)=" }{TEXT 327 3 "phi" }{TEXT -1 6 "(0) \350 " }{TEXT 328 1 "u" }{TEXT -1 1 "(" }{TEXT 331 1 "L" }{TEXT -1 4 ",0)=" }{TEXT 329 1 "f" }{TEXT -1 1 "(" }{TEXT 333 1 "L" }{TEXT -1 2 ")=" }{TEXT 330 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)=phi(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 14 "g:=(x,t)->-2; " }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"gGf*6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF)! \"#F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "\317\360\350 \375 \362\356\354 0<" }{TEXT 285 1 "x" }{TEXT -1 1 "<" }{TEXT 286 1 "L" } {TEXT -1 2 ", " }{TEXT 287 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 441 1 "u " }{TEXT -1 1 "(" }{TEXT 442 1 "x" }{TEXT -1 1 "," }{TEXT 443 1 "t" } {TEXT -1 2 ")=" }{TEXT 444 1 "z" }{TEXT -1 1 "(" }{TEXT 445 1 "x" } {TEXT -1 1 "," }{TEXT 446 1 "t" }{TEXT -1 2 ")+" }{TEXT 452 1 "w" } {TEXT -1 1 "(" }{TEXT 447 1 "x" }{TEXT -1 1 "," }{TEXT 448 1 "t" } {TEXT -1 2 ")+" }{TEXT 449 1 "v" }{TEXT -1 1 "(" }{TEXT 450 1 "x" } {TEXT -1 1 "," }{TEXT 451 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 468 1 "u" }{TEXT -1 1 "(" }{TEXT 469 1 "x" } {TEXT -1 1 "," }{TEXT 470 1 "t" }{TEXT -1 9 "), \352\360\356\354\345 \+ " }{TEXT 575 1 "z" }{TEXT -1 1 "(" }{TEXT 576 1 "x" }{TEXT -1 1 "," } {TEXT 577 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 429 1 "z" }{TEXT -1 1 "(" }{TEXT 430 1 "x" }{TEXT -1 1 "," }{TEXT 431 1 "t" }{TEXT -1 10 ") \360\345\370\345\355\350\377 " }{TEXT 432 1 "u" } {TEXT -1 1 "(" }{TEXT 433 1 "x" }{TEXT -1 1 "," }{TEXT 434 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 440 1 "w" }{TEXT -1 1 "(" }{TEXT 435 1 "x" }{TEXT -1 1 "," }{TEXT 436 1 "t" } {TEXT -1 15 ") \350\347 \363\360\340\342\355\345\355\350\377:" }}} {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "dew:=a^2*diff(w(x,t),x$2)-diff (w(x,t),t$2)=0:" "6#>%$dewG/,&*&%\"aG\"\"#-%%diffG6$-%\"wG6$%\"xG%\"tG -%\"$G6$F0F)\"\"\"F5-F+6$-F.6$F0F1-F36$F1F)!\"\"\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "\312\356\354\357\356\355\345\355\362\363 \+ " }{TEXT 437 1 "v" }{TEXT -1 1 "(" }{TEXT 438 1 "x" }{TEXT -1 1 "," } {TEXT 439 1 "t" }{TEXT -1 29 ") \350\347 \363\360\340\342\355\345\355 \350\377, \344\353\377 \352\356\362\356\360\356\343\356 " }{TEXT 453 1 "g" }{TEXT -1 2 "1(" }{TEXT 454 1 "x" }{TEXT -1 1 "," }{TEXT 455 1 " t" }{TEXT -1 24 ") \341\363\344\345\362 \356\357\360\345\344\345\353 \345\355\340 \355\350\346\345." }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "a^2*diff(v(x,t),x$2)-diff(v(x,t),t$2)+g1(x,t)=0:" "6#/,(*&%\"aG \"\"#-%%diffG6$-%\"vG6$%\"xG%\"tG-%\"$G6$F.F'\"\"\"F3-F)6$-F,6$F.F/-F1 6$F/F'!\"\"-%#g1G6$F.F/F3\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 300 26 "1. \307\340\357\350\370\345\354 1-\376 \352\356\354\357\356\355 \345\355\362\363 " }{TEXT 334 1 "z" }{TEXT 337 1 "(" }{TEXT 335 1 "x" }{TEXT 338 1 "," }{TEXT 336 1 "t" }{TEXT 339 10 ") \360\345\370\345 \355\350\377 " }{TEXT 292 1 "u" }{TEXT 301 1 "(" }{TEXT 293 1 "x" } {TEXT 302 1 "," }{TEXT 294 1 "t" }{TEXT 303 1 ")" }{TEXT -1 1 ":" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "z(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "\317\356 \361\362\360\356\350\354 \343\360\340\364\350\352 \375\362\356\351 \+ \364\363\355\352\366\350\350" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "plot3d(z(x,t), x=0..L+2, t=0..6,axes=boxed,orientation=[-33,56]) ;" }}{PARA 13 "" 1 "" {GLPLOT3D 494 165 165 {PLOTDATA 3 "6&-%%GRIDG6%; 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}{TEXT 369 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "v:=(x,t)->sum((int(q(n,tau)*sin(b(n)*a*(t-tau)), tau=0. .t)*Xn(x,n)/(b(n)*a)), n=1..N): simplify(v(x,t));" "6#C$>%\"vGf*6$%\"x G%\"tG7\"6$%)operatorG%&arrowG6\"-%$sumG6$*(-%$intG6$*&-%\"qG6$%\"nG%$ tauG\"\"\"-%$sinG6#*(-%\"bG6#F:F<%\"aGF<,&F)F " 0 "" {MPLTEXT 1 0 7 "v(0,0); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 316 51 "4. \310\362\340\352, \350\354\345\345\354 \360\345\370 \345\355\350\345 \344\350\364\364\345\360\345\355\366\350\340\353\374 \355\356\343\356 \363\360\340\342\355\345\355\350\377 " }{TEXT 315 2 " de" }{TEXT 317 21 " \342 \356\352\356\355\367\340\362\345\353\374\355 \356\354 \342\350\344\345" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 57 "U:=(x,t)->z(x,t)+W(x,t)+v(x,t); U(x,t):=simplify(U( x,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UGf*6$%\"xG%\"tG6\"6$%)o peratorG%&arrowGF),(-%\"zG6$9$9%\"\"\"-%\"WGF0F3-%\"vGF0F3F)F)F)" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"UG6$%\"xG%\"tG-%$sumG6$,$*,\"\"% \"\"\",*-%$cosG6#*(%#PiGF/%\"nGF/F(F/!\"\"*&F1F/)F7F6F/F/F/F/F9F7F/F5! \"$F6F:-%$sinG6#*(F5F/F6F/F'F/F/F7/F6;F/%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "*) \327\362\356\341\373 \347\340\357\350\361 \340\362\374 " }{TEXT 598 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 418 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 0 103 "NN:=20: Un:=(x,t)->sum(-4*( -cos(Pi*n*t)+cos(Pi*n*t)*(-1)^n+1-(-1)^n)/Pi^3/n^3*sin(Pi*n*x),n = 1 . . NN);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#UnGf*6$%\"xG%\"tG6\"6$%)o peratorG%&arrowGF)-%$sumG6$,$*,\"\"%\"\"\",*-%$cosG6#*(%#PiGF3%\"nGF39 %F3!\"\"*&F5F3)FF " 0 "" {MPLTEXT 1 0 29 "re:=subs(u(x,t)=Un(x,t),de ): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 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 419 2 "Un" }{TEXT -1 1 "(" }{TEXT 420 1 "x" }{TEXT -1 1 "," }{TEXT 421 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 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