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"" {TEXT -1 32 "\361 \353\345\344\363\345\362 \356\362\352\360\373\362\374, \361\355\377 \342 \340\357\356\361\362\360\356\364\373." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 49 "u(0,t):=phi(t); u(L,t):=psi(t); " }{TEXT -1 2 "1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"uG6$\"\"!%\"tG ,$*&\"#g\"\"\"F(F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"uG6$\"\" \"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "`D[1](u)(0, t):=phi(t); D[1](u)(L,t):=psi(t);`: " }{TEXT -1 2 "2)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "`D[1](u)(0,t):=phi(t); u(L,t):=psi( t);`: " }{TEXT -1 2 "3)" }{MPLTEXT 1 0 4 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "`u(0,t):=phi(t); D[1](u)(L,t):=psi( t);`: " }{TEXT -1 17 " 4)" }{MPLTEXT 1 0 1 " " }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "\317\360\356\342\345\344\345\354 \+ \361\345\354\340\355\362\350\367\345\361\352\356\345 \352\356\355\342 \345\360\362\350\360\356\342\340\355\350\345 \356\357\345\360\340\362 \356\360\340 " }{TEXT 531 1 "D" }{TEXT -1 3 " \342 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-1 1 "," }{TEXT 554 1 "t" }{TEXT -1 26 ") \342 \+ \340\355\340\353\356\343\350\367\355\373\365 \362\356\367\352\340\365, \362\356" }}{PARA 0 "" 0 "" {TEXT -1 32 "\345\361\362\374 \350\365 \+ \360\340\347\355\356\361\362\374 \360\340\342\355\377\353\340\361\374 \+ \355\363\353\376." }}{PARA 256 "" 0 "" {TEXT -1 72 "\321\364\356\360 \354\350\360\363\345\354 \353\356\343\350\367\345\361\352\350\351 \341 \353\356\352 \342\373\341\356\360\340 \362\350\357\340 \343\360\340 \355\350\367\355\373\365 \363\361\353\356\342\350\351, \352\356\362 \356\360\373\345 \341\363\344\363\362 " }}{PARA 258 "" 0 "" {TEXT -1 57 "\356\357\360\345\344\345\353\377\362\374 (\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 526 1 "b" }{TEXT -1 1 "(" }{TEXT 527 1 "n" }{TEXT -1 16 ") \+ \350 \361\356\341\361\362\342\345\355\355\373\345 " }}{PARA 259 "" 0 " " {TEXT -1 8 "\364\363\355\352\366\350\350 " }{TEXT 528 2 "Xn" }{TEXT -1 1 "(" }{TEXT 529 1 "x" }{TEXT -1 1 "," }{TEXT 530 1 "n" }{TEXT -1 3 "), " }{TEXT 620 50 "\340 \362\340\352\346\345 \357\356\344\341\350 \360\340\345\354\363\376 \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 533 1 "z" }{TEXT 621 1 "(" }{TEXT 534 1 "x" }{TEXT 622 1 "," } {TEXT 535 1 "t" }{TEXT 623 1 ")" }{TEXT -1 1 ":" }}}{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 -%$psiG6#F(F2F2F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "\317\360\356\342\345\344\345\354 \+ \342\350\347\363\340\353\350\347\340\366\350\376 \342\373\341\360\340 \355\355\373\365 \361\356\341\361\362\342\345\355\355\373\365 \347\355 \340\367\345\355\350\351 " }{TEXT 521 1 "b" }{TEXT -1 1 "(" }{TEXT 522 1 "n" }{TEXT -1 23 "), \361\356\341\361\362\342\345\355\355\373 \365 \364\363\355\352\366\350\351 " }}{PARA 0 "" 0 "" {TEXT 523 2 "Xn " }{TEXT -1 1 "(" }{TEXT 524 1 "x" }{TEXT -1 1 "," }{TEXT 525 1 "n" } {TEXT -1 12 ") \350 \364\363\355\352\366\350\350 " }{TEXT 536 1 "z" } {TEXT -1 1 "(" }{TEXT 537 1 "x" }{TEXT -1 1 "," }{TEXT 538 1 "t" } {TEXT -1 56 "), \361\356\356\362\342\345\362\361\362\342\363\376\371 \350\365 \362\350\357\363 \352\360\340\345\342\373\365 \363\361\353 \356\342\350\351 \347\340\344\340\367\350 (\352\356\362\356\360\373 \345 " }}{PARA 0 "" 0 "" {TEXT -1 39 "\342\373\341\360\340\355\373 \+ \350 \345\361\362\374 \355\340 \357\360\345\344\373\344\363\371\345 \351 \361\362\360\340\355\350\366\345)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "b(n);Xn(x,n); z(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%#PiG\"\"\"%\"nGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6 #*(%#PiG\"\"\"%\"nGF(%\"xGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\" #g\"\"\"%\"tGF&F&*(F%F&%\"xGF&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 "Ww(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$\"\"!%\"tG,&--F&6#%\"uGF,F)*&\"#gF)F.F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$F)%\"tG,&--F&6#%\"uGF,F)*& \"#gF)F-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$\"\"!%\" tG,&--F&6#%\"uGF,F)*&\"#gF)F.F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ -%#WwG6$\"\"\"%\"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)*&\"#gF)F-F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 310 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 317 1 " " }} {PARA 0 "" 0 "" {TEXT 572 1 "u" }{TEXT -1 6 "(0,0)=" }{TEXT 311 1 "f" }{TEXT -1 4 "(0)=" }{TEXT 312 3 "phi" }{TEXT -1 7 "(0) \350 " }{TEXT 313 1 "u" }{TEXT -1 1 "(" }{TEXT 316 1 "L" }{TEXT -1 4 ",0)=" }{TEXT 314 1 "f" }{TEXT -1 1 "(" }{TEXT 318 1 "L" }{TEXT -1 2 ")=" }{TEXT 315 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 "" {MPLTEXT 1 0 21 "`assume (t,negative)`:" }}}{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 24 "g:=(x,t)->36*x*t*(L-x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG f*6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF),$**\"#O\"\"\"9$F09%F0,&%\"LGF 0F1!\"\"F0F0F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "\317\360 \350 \375\362\356\354 0<" }{TEXT 274 1 "x" }{TEXT -1 1 "<" }{TEXT 275 1 "L" }{TEXT -1 2 ", " }{TEXT 276 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 66 "\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 403 1 "u" }{TEXT -1 1 "(" }{TEXT 404 1 "x" }{TEXT -1 1 "," } {TEXT 405 1 "t" }{TEXT -1 2 ")=" }{TEXT 406 1 "z" }{TEXT -1 1 "(" } {TEXT 407 1 "x" }{TEXT -1 1 "," }{TEXT 408 1 "t" }{TEXT -1 2 ")+" } {TEXT 414 1 "w" }{TEXT -1 1 "(" }{TEXT 409 1 "x" }{TEXT -1 1 "," } {TEXT 410 1 "t" }{TEXT -1 2 ")+" }{TEXT 411 1 "v" }{TEXT -1 1 "(" } {TEXT 412 1 "x" }{TEXT -1 1 "," }{TEXT 413 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$2)-diff(u(x,t),t)+g(x,t)=0:" "6#>%#deG/,(*&%\"aG\"\"#-%%diffG6$- %\"uG6$%\"xG%\"tG-%\"$G6$F0F)\"\"\"F5-F+6$-F.6$F0F1F1!\"\"-%\"gG6$F0F1 F5\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "\317\360\350\354\345 \367\340\355\350\345. \323\360\340\342\355\345\355\350\345 de \357\360 \350 a = 1, L = 1 \361\356\342\357\340\344\340\345\362 \361 \363\360 \340\342\355\345\355\350\345\354 (1.1) \350\347 \314\323 \"\320\345 \370\345\355\350\345" }}{PARA 0 "" 0 "" {TEXT -1 84 "\347\340\344\340 \367 \323\314\324 \342 Mathcad\", \344\353\377 \352\356\362\356\360 \356\343\356 \362\340\354 \346\345 \357\356\353\363\367\345\355\356 \+ \360\345\370\345\355\350\345 (1.4). \302 \352\356\355\366\345 7.3.1. \+ \354\373 " }}{PARA 0 "" 0 "" {TEXT -1 32 "\357\360\356\342\345\344\345 \354 \361\360\340\342\355\345\355\350\345 \375\362\350\365 \360\345 \370\345\355\350\351." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "\304\353 \377 \352\340\346\344\356\351 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" }}{PARA 0 "" 0 "" {TEXT 596 12 "\316\357\360\345\344 \345\353\345\355\350\345 " }{TEXT 593 2 "vn" }{TEXT 597 1 "(" }{TEXT 594 1 "x" }{TEXT 598 1 "," }{TEXT 595 1 "t" }{TEXT 599 13 ") \352\340 \352 \364\363\355\352\366\350\350" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 25 "\317\360\345\346\344\345 \342\373\367\350\361\353\350\354 \350\355\362\345\343\360\340\353 " }{TEXT 600 3 "ImT" }{TEXT -1 1 "( " }{TEXT 601 1 "m" }{TEXT -1 1 "," }{TEXT 602 1 "t" }{TEXT -1 25 ") \+ \352\340\352 \364\363\355\352\366\350\376 \357\345\360\345\354\345\355 \355\373\365 " }{TEXT 603 1 "m" }{TEXT -1 2 ", " }{TEXT 604 1 "t" } {TEXT -1 18 ", \356\344\355\340 \350\347 \352\356\362\356\360\373\365 \+ " }{TEXT 605 1 "m" }}{PARA 0 "" 0 "" {TEXT -1 22 "\377\342\353\377\345 \362\361\377 \366\345\353\356\367\350\361\353\345\355\355\356\351" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "ImT:=(m,t)->int(q(m,tau)*exp (-(b(m)*a)^2*(t-tau)), tau=0..t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$ImTGf*6$%\"mG%\"tG6\"6$%)operatorG%&arrowGF)-%$intG6$*&-%\"qG6$9$%$t auG\"\"\"-%$expG6#,$*()-%\"bG6#F4\"\"#F6)%\"aGF@F6,&9%F6F5!\"\"F6FEF6/ F5;\"\"!FDF)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "\302\342\345 \344\270\354 \356\343\360\340\355\350\367\345\355\350\345 \361\354\354 \350\360\356\342\340\355\350\377 " }{TEXT 606 2 "NN" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "NN:=20:assume(m,integer):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 43 "\316\357\360\345\344\345\353\350\354 \352\356\354 \357\356\355\345\355\362\363 \342\345\352\362\356\360\340 sv \352\340 \352 \364\363\355\352\366\350\376" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "sv:=(x,t)->vector(NN,[seq(ImT(m,t)*Xn(x,m),m=1..NN)]) :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "\350 \357\360\356\342\345 \344\270\354 \345\270 \342\373\367\350\361\353\345\355\350\345" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "eval(sv(x,t)): sv(x,t)[2]; s v(0.5,1)[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"#:\"\"\",&F&!\" \"-%$expG6#,$*(\"\"%F&)%#PiG\"\"#F&%\"tGF&F&F&F&F0!\"$-F*6#,$*(F.F&F/F &F2F&F(F&-%$sinG6#,$*(F1F&F0F&%\"xGF&F&F&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "\316\357 \360\345\344\345\353\350\354 \361\340\354\363 \364\363\355\352\366\350 \376 " }{TEXT 607 2 "vn" }{TEXT -1 1 "(" }{TEXT 608 1 "x" }{TEXT -1 1 "," }{TEXT 609 1 "t" }{TEXT -1 1 ")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "vn:=(x,t)->sum(sv(x,t)[j], j=1..NN); vn(x,t):" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vnGf*6$%\"xG%\"tG6\"6$%)operatorG%& arrowGF)-%$sumG6$&-%#svG6$9$9%6#%\"jG/F7;\"\"\"%#NNGF)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "\302 \352\340\367\345\361\362\342\345 \+ \357\360\356\342\345\360\352\350 \342\373\367\350\361\353\350\354 \347 \355\340\367\345\355\350\345 \364\363\355\352\366\350\350 " }{TEXT 610 2 "vn" }{TEXT -1 1 "(" }{TEXT 611 1 "x" }{TEXT -1 1 "," }{TEXT 612 1 "t" }{TEXT -1 10 ") \342 \362\356\367\352\345 " }{TEXT 613 2 "vn " }{TEXT -1 5 "(0,0)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "vn(0 ,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 304 51 "4. \310\362\340\352, \350\354\345\345\354 \360\345 \370\345\355\350\345 \344\350\364\364\345\360\345\355\366\350\340\353 \374\355\356\343\356 \363\360\340\342\355\345\355\350\377 " }{TEXT 303 2 "de" }{TEXT 305 21 " \342 \356\352\356\355\367\340\362\345\353 \374\355\356\354 \342\350\344\345" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 57 "U:=(x,t)->z(x,t)+W(x,t)+v(x,t); U(x,t):=simp lify(U(x,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UGf*6$%\"xG%\"tG6 \"6$%)operatorG%&arrowGF),(-%\"zG6$9$9%\"\"\"-%\"WGF0F3-%\"vGF0F3F)F)F )" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"UG6$%\"xG%\"tG,**&\"#g\"\"\" F(F,F,*(F+F,F'F,F(F,!\"\"-%$sumG6$,$*.\"#7F,)F.,&F,F,%#n|irGF,F,%#PiG! \"$F7F9-%$expG6#,$*()F8\"\"#F,)F7F@F,F(F,F.F,-%$sinG6#*(F8F,F7F,F'F,F, F,/F7;F,%)infinityGF,-F06$,$*.\"#CF,,2*(\"\"&F,)F8\"\"%F,)F7FRF,F.\"\" 'F.*&FTF,)F.F7F,F,**FPF,-F;6#F>F,FQF,FSF,F,*&FTF,FXF,F,*(FTF,F5F,FXF,F ,*,FTF,FXF,F?F,FAF,F(F,F.*.FTF,FXF,F?F,FAF,F(F,FVF,F,F,F8!\"(F7FhnF:F, FBF,F.FFF," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "\317\360\356\342 \345\344\345\354 \357\360\345\356\341\360\340\347\356\342\340\355\350 \377 (\355\345\356\341\377\347\340\362\345\353\374\355\340\377 \367 \340\361\362\374 \360\345\370\345\355\350\377). " }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "p:=(-5*Pi^4*n^4-6+6*(-1)^n+5*exp(Pi^2*n^2*t)*Pi ^4*n^4+6*exp(Pi^2*n^2*t)+6*(-1)^(1+n)*exp(Pi^2*n^2*t)-6*exp(Pi^2*n^2*t )*Pi^2*n^2*t+6*exp(Pi^2*n^2*t)*Pi^2*n^2*t*(-1)^n)*exp(-Pi^2*n^2*t):" " 6#>%\"pG*&,2*(\"\"&\"\"\"*$%#PiG\"\"%F)*$%\"nGF,F)!\"\"\"\"'F/*&F0F)), $F)F/F.F)F)**F(F)-%$expG6#*(F+\"\"#*$F.F9F)%\"tGF)F)*$F+F,F)*$F.F,F)F) *&F0F)-F66#*(F+F9*$F.F9F)F;F)F)F)*(F0F)),$F)F/,&F)F)F.F)F)-F66#*(F+F9* $F.F9F)F;F)F)F)*,F0F)-F66#*(F+F9*$F.F9F)F;F)F)*$F+F9F)*$F.F9F)F;F)F/*. 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NN)+sum(-24*(-5*Pi^ 4*n^4-6+6*(-1)^n+5*exp(Pi^2*n^2*t)*Pi^4*n^4+6*exp(Pi^2*n^2*t)+6*(-1)^( 1+n)*exp(Pi^2*n^2*t)-6*exp(Pi^2*n^2*t)*Pi^2*n^2*t+6*exp(Pi^2*n^2*t)*Pi ^2*n^2*t*(-1)^n)/Pi^7/n^7*exp(-Pi^2*n^2*t)*sin(Pi*n*x),n = 1 .. NN):UN (x,t):=simplify(UN(x,t)):" "6#C$>%#UNGf*6$%\"xG%\"tG7\"6$%)operatorG%& arrowG6\",**&\"#g\"\"\"F)F2F2*(F1F2F(F2F)F2!\"\"-%$sumG6$*.\"#7F2),$F2 F4,&F2F2%\"nGF2F2*$%#PiG\"\"$F4*$F=F@F4-%$expG6#,$*(F?\"\"#*$F=FGF2F)F 2F4F2-%$sinG6#*(F?F2F=F2F(F2F2/F=;F2%#NNGF2-F66$,$*.\"#CF2,2*(\"\"&F2* $F?\"\"%F2*$F=FYF2F4\"\"'F4*&FenF2),$F2F4F=F2F2**FWF2-FC6#*(F?FG*$F=FG F2F)F2F2*$F?FYF2*$F=FYF2F2*&FenF2-FC6#*(F?FG*$F=FGF2F)F2F2F2*(FenF2),$ F2F4,&F2F2F=F2F2-FC6#*(F?FG*$F=FGF2F)F2F2F2*,FenF2-FC6#*(F?FG*$F=FGF2F )F2F2*$F?FGF2*$F=FGF2F)F2F4*.FenF2-FC6#*(F?FG*$F=FGF2F)F2F2*$F?FGF2*$F =FGF2F)F2),$F2F4F=F2F2F2*$F?\"\"(F4*$F=F^qF4-FC6#,$*(F?FG*$F=FGF2F)F2F 4F2-FJ6#*(F?F2F=F2F(F2F2F4/F=;F2FOF2F.F.F.>-F%6$F(F)-%)simplifyG6#-F%6 $F(F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "\362\356 \357\356\353 \363\367\350\354 \341\356\353\345\345 \352\356\354\357\340\352\362\355 \363\376 \350 \341\373\361\362\360\363\376 \364\356\360\354\363\353 \363 \361\367\345\362\340, \355\356 \342\361\377\352\350\351 \360\340 \347 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\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 377 1 "U" }{TEXT -1 1 "(" } {TEXT 378 1 "x" }{TEXT -1 1 "," }{TEXT 379 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 58 "re:=subs(u(x,t)=Un(x,t),de ): rep:=subs(u(x,t)=sp(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 83 "\355 \350\377, \342 \360\345\347\363\353\374\362\340\362\345 \352\356\362 \356\360\356\351 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