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" }}{PARA 0 "" 0 "" {TEXT -1 45 " \315\340\367\355\345\354 \361 \342\373\367\350\361\353\345\355\350\377 \352\356\375\364\364\350\366\350\345\355\362\356\342 \360\377\344\340 \324\363\360\374\345:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "- \347 \340\357\350\370\345\354 \352\356\375\364\364\350\366\350\345\355\362 \373 \360\377\344\340 \324\363\360\374\345 \344\353\377 \364\363\355 \352\366\350\351 \355\340\367\340\353\374\355\373\365 \363\361\353\356 \342\350\351:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "A:=n->2/L*in t(f1(x)*sin(Pi*n*x/L), x=0..L): A(n);" "6#C$>%\"AGf*6#%\"nG7\"6$%)oper atorG%&arrowG6\"*(\"\"#\"\"\"%\"LG!\"\"-%$intG6$*&-%#f1G6#%\"xGF0-%$si nG6#**%#PiGF0F(F0F:F0F1F2F0/F:;\"\"!F1F0F-F-F--F%6#F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"%\"\"\",&F&!\"\")F(%#n|irGF&F&%#PiG!\"$F*F ,F(" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "B:=n->2/(Pi*n*a)*int(F 1(x)*sin(Pi*n*x/L), x=0..L): B(n);" "6#C$>%\"BGf*6#%\"nG7\"6$%)operato rG%&arrowG6\"*(\"\"#\"\"\"*(%#PiGF0F(F0%\"aGF0!\"\"-%$intG6$*&-%#F1G6# %\"xGF0-%$sinG6#**F2F0F(F0F " 0 " " {XPPEDIT 19 1 "W:=(x,t)->sum((A(n)*cos(omegan*t)+B(n)*sin(omegan*t)) *sin(Pi*n*x/L), n=1..N):W(x,t);" "6#C$>%\"WGf*6$%\"xG%\"tG7\"6$%)opera torG%&arrowG6\"-%$sumG6$*&,&*&-%\"AG6#%\"nG\"\"\"-%$cosG6#*&%'omeganGF 9F)F9F9F9*&-%\"BG6#F8F9-%$sinG6#*&F>F9F)F9F9F9F9-FD6#**%#PiGF9F8F9F(F9 %\"LG!\"\"F9/F8;F9%\"NGF.F.F.-F%6$F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sumG6$,$*.\"\"%\"\"\",&F)!\"\")F+%#n|irGF)F)%#PiG!\"$F-F/-%$c osG6#*(F.F)F-F)%\"tGF)F)-%$sinG6#*(F.F)F-F)%\"xGF)F)F+/F-;F)%)infinity G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 309 48 "\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 308 2 "de" }{TEXT 310 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 25 "W(x,t):=simplify(W(x,t));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"WG6$%\"xG%\"tG-%$sumG6$,$*.\"\"% \"\"\",&F/!\"\")F1%#n|irGF/F/%#PiG!\"$F3F5-%$cosG6#*(F4F/F3F/F(F/F/-%$ sinG6#*(F4F/F3F/F'F/F/F1/F3;F/%)infinityG" }}}{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 358 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 84 "NN:=20: Wn:=(x,t)->sum(-4*(-1+(-1)^n)/Pi^3/n^3*cos(Pi*n*t)*sin (Pi*n*x),n = 1 .. NN);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#WnGf*6$% \"xG%\"tG6\"6$%)operatorG%&arrowGF)-%$sumG6$,$*.\"\"%\"\"\",&F3!\"\")F 5%\"nGF3F3%#PiG!\"$F7F9-%$cosG6#*(F8F3F7F39%F3F3-%$sinG6#*(F8F3F7F39$F 3F3F5/F7;F3%#NNGF)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 311 8 "\317 \360\356\342\345\360\352\340" }{TEXT -1 31 ". \317\356\344\361\362\340 \342\350\354 \357\356\353\363\367\345\355\355\356\345 \360\345\370\345 \355\350\345 " }{TEXT 359 1 "W" }{TEXT -1 1 "(" }{TEXT 360 1 "x" } {TEXT -1 1 "," }{TEXT 361 1 "t" }{TEXT -1 38 ") \342 \350\361\365\356 \344\355\356\345 \344\350\364\364\345\360\345\355\366\350\340\353\374 \355\356\345 \363\360\340\342\355\345-" }}{PARA 0 "" 0 "" {TEXT -1 4 " \355\350\345 " }{TEXT 257 2 "de" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "re:=subs(w(x,t)=W(x,t),de): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "\302 \357\360\340\342\350\353\374\355\356\361 \362\350 \357\356\353\363\367\345\355\355\356\343\356 \360\345\370\345 \355\350\377 \354\356\346\355\356 \363\341\345\344\350\362\374\361\377 , \347\340\357\363\361\362\350\342 \357\360\356\366\345\344\363\360 \363 \363\357\360\356\371\345-" }}{PARA 0 "" 0 "" {TEXT -1 82 "\355 \350\377, \342 \360\345\347\363\353\374\362\340\362\345 \352\356\362 \356\360\356\351 \344\356\353\346\355\373 \357\356\353\363\367\350\362 \374 \362\356\346\344\345\361\362\342\356 \350\353\350 \350\347-\347 \340 \356\343\360\340\355\350\367\345\355\355\356\343\356 \367\350\361 \353\340 " }}{PARA 0 "" 0 "" {TEXT -1 45 "\367\353\345\355\356\342 \+ \360\377\344\340 \362\356\353\374\352\356 \357\360\350\341\353\350\347 \350\362\345\353\374\355\356\345 \362\356\346\344\345\361\362\342\356. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(re);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!F$" }}}{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 362 2 "Wn" } {TEXT -1 1 "(" }{TEXT 363 1 "x" }{TEXT -1 1 "," }{TEXT 364 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(w(x,t)=Wn(x,t),de) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "plot3d(lhs(ren), x=0.. 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