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" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "\316\341\360\340\362\350\354 \+ \342\355\350\354\340\355\350\345 \355\340 \361\345\354\340\355\362\350 \352\363 \356\357\366\350\350 " }{TEXT 293 6 "assume" }{TEXT -1 38 ", \+ \363\352\340\347\373\342\340\376\371\345\351 \355\340 \361\342\356\351 \361\362\342\340 \357\340\360\340\354\345\362\360\356\342, " }}{PARA 0 "" 0 "" {TEXT -1 80 "\363\367\340\361\362\342\363\376\371\350\365 \+ \342 \342\373\367\350\361\353\345\355\350\377\365. \301\363\344\345 \354 \350\361\357\356\353\374\347\356\342\340\362\374 \375\362\363 \+ \356\357\366\350\376 \357\360\350 \363\357\360\356\371\345\355\350\350 \342\373\360\340\346\345\355\350\351." }}{PARA 0 "" 0 "" {TEXT -1 29 "\323\352\340\346\345\354 \355\340 \361\342\356\351\361\362\342\356 \+ \357\340\360\340\354\345\362\360\340 " }{TEXT 291 1 "n" }{TEXT -1 22 " \350 \342\342\345\344\345\354 \356\341\356\347\355\340\367\345\355 \350\377:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "assume(n,integ er): omegan:=Pi*n*a/L: N:=infinity:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "\317\360\350\354\345\360 \361\356\341\361\362\342\345\355\355 \356\351 \364\363\355\352\366\350\350:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fs:=x->sin(Pi*n*x/L);fs(1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fsGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%$sinG6#**%#P iG\"\"\"%\"nGF19$F1%\"LG!\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%$sinG6#,$*(\"\"#!\"\"%#PiG\"\"\"%#n|irGF+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "\323\352\340\346\345\354 \355\340 \360\377\344 \357 \340\360\340\354\345\362\360\356\342 \347\340\344\340\367\350 - \361 \356\341\361\362\342\345\355\355\373\345 \367\350\361\353\340 \350 \+ \361\356\341\361\362\342\345\355\355\373\345 \364\363\355\352\366\350 \350" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 " b:=(n)->Pi*n/L; X n:=(x,n)->sin(b(n)*x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGf*6#% \"nG6\"6$%)operatorG%&arrowGF(*(%#PiG\"\"\"9$F.%\"LG!\"\"F(F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#XnGf*6$%\"xG%\"nG6\"6$%)operatorG%& arrowGF)-%$sinG6#*&-%\"bG6#9%\"\"\"9$F5F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "\302\345\360\355\345\354\361\377 \352 \357\360\345\346 \355\350\354 \347\355\340\367\345\355\350\377\354" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 7 "n:='n':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "\322\345\357\345\360\374 \347\340\357\350\370\345\354 \342\373\360 \340\346\345\355\350\345 2-\351 \352\356\354\357\356\355\345\355\362 \373 \357\356\344 \350\354\345\355\345\354 " }{TEXT 342 1 "W" }{TEXT -1 1 "(" }{TEXT 343 1 "x" }{TEXT -1 1 "," }{TEXT 344 1 "t" }{TEXT -1 9 ") \342\354\345\361\362\356 " }{TEXT 345 1 "w" }{TEXT -1 1 "(" } {TEXT 346 1 "x" }{TEXT -1 1 "," }{TEXT 347 1 "t" }{TEXT -1 15 "), \344 \353\377 \352\356\362\356\360\356\351 " }}{PARA 0 "" 0 "" {TEXT -1 27 "\347\340\357\350\370\345\354 \361\353\345\344\363\376\371\363\376 \+ \364\356\360\354\363\353\363: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "W:=(x,t)->sum((A(n)*cos(b(n)*a*t)+B(n)*sin(b(n)*a*t))*Xn(x,n), n = 1 .. N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"WGf*6$%\"xG%\"tG6 \"6$%)operatorG%&arrowGF)-%$sumG6$*&,&*&-%\"AG6#%\"nG\"\"\"-%$cosG6#*( -%\"bGF5F7%\"aGF79%F7F7F7*&-%\"BGF5F7-%$sinGF:F7F7F7-%#XnG6$9$F6F7/F6; F7%\"NGF)F)F)" }}}{EXCHG {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 73 "- \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 \347\340\344\340\355\355\373\365 \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*int(f1(x)*sin(Pi*n*x/L), x=0..L): A(n); " "6# C$>%\"AGf*6#%\"nG7\"6$%)operatorG%&arrowG6\"*(\"\"#\"\"\"%\"LG!\"\"-%$ intG6$*&-%#f1G6#%\"xGF0-%$sinG6#**%#PiGF0F(F0F:F0F1F2F0/F:;\"\"!F1F0F- F-F--F%6#F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"#\"\"\",(F%!\" \"*(%#PiGF&%\"nGF&-%$sinG6#*&F*F&F+F&F&F&*&F%F&-%$cosGF.F&F&F&F*!\"$F+ F3F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "\302\373\367\350\361\353 \350\354 \350 \357\360\345\344\361\362\340\342\350\354 A(n) \352\340 \352 \352\356\354\357\340\355\345\355\362\373 \342\345\352\362\356\360 \340 AA[n]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "N3:=10: " } {TEXT -1 17 "- \367\350\361\353\356 \352\356\354\357\340\355\345\355 \362" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for nn from 1 to N3 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "AA[nn]:=limit(A(k), k=nn):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "AA:=convert(AA,list); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AAG7,,$*&\"\")\"\"\"%#PiG!\"$F)\"\"!,$*(F(F)\"#F!\"\"F*F+F)F, ,$*(F(F)\"$D\"F0F*F+F)F,,$*(F(F)\"$V$F0F*F+F)F,,$*(F(F)\"$H(F0F*F+F)F, " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "\304\360\363\343\356\351 \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 \355\340\367\340\353\374\355\373\365 \363\361\353\356\342\350\351:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "B:=n->2/(Pi*n*a)*int(F1(x)*sin(Pi*n*x/L), x=0..L): B(n); " "6#C$ >%\"BGf*6#%\"nG7\"6$%)operatorG%&arrowG6\"*(\"\"#\"\"\"*(%#PiGF0F(F0% \"aGF0!\"\"-%$intG6$*&-%#F1G6#%\"xGF0-%$sinG6#**F2F0F(F0F " 0 "" {MPLTEXT 1 0 22 "for nn from 1 to N 3 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "BB[nn]:=limit(B(k), k=nn): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "BB:=convert(BB,list); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BBG7,,$*&\"\"$\"\"\"%#PiG!\"\"F)\"\"!F,F,F,F,F,F,F,F ," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "\321\353\345\344\356\342\340 \362\345\353\374\355\356, \345\361\362\374 \345\344\350\355\361\362 \342\345\355\355\356\345 \347\355\340\367\345\355\350\345 B(n) \356 \362\353\350\367\355\356\345 \356\362 \355\363\353\377 - \375\362\356 \+ " }{TEXT 336 1 "B" }{TEXT -1 8 "(1) = 3/" }{TEXT 337 2 "Pi" }{TEXT -1 2 ". 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