{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 16 "Fourierova \370ada:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "a:=(f,n)->1/Pi*int(f(x)*cos (n*x),x=-Pi..Pi);\nb:=(f,n)->1/Pi*int(f(x)*sin(n*x),x=-Pi..Pi);\nxxx:= (f,N)-> unapply(a(f,0)/2+sum(a(f,i)*cos(i*x)+b(f,i)*sin(i*x),i=1..N),x );\nxxx(x->x^2+3*x,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGj+6$% \"fG%\"nG6\"6$%)operatorG%&arrowGF),$-%$intG6$*&-9$6#%\"xG\"\"\"-%$cos G6#*&9%F6F5F6F6/F5;,$%#PiG!\"\"F?*$F?F@F)F)F)6$\"\"!FC" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGj+6$%\"fG%\"nG6\"6$%)operatorG%&arrowGF),$-% $intG6$*&-9$6#%\"xG\"\"\"-%$sinG6#*&9%F6F5F6F6/F5;,$%#PiG!\"\"F?*$F?F@ F)F)F)6$\"\"!FC" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xxxGj+6$%\"fG%\" NG6\"6$%)operatorG%&arrowGF)-%(unapplyG6$,&*&#\"\"\"\"\"#F3-%\"aG6$9$ \"\"!F3F3-%$sumG6$,&*&-F66$F8%\"iGF3-%$cosG6#*&FAF3%\"xGF3F3F3*&-%\"bG F@F3-%$sinGFDF3F3/FA;F39%F3FFF)F)F)6$F9F9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#j+6#%\"xG6\"6$%)operatorG%&arrowGF&,0*&\"\"$!\"\"%#PiG \"\"#\"\"\"*&\"\"%F0-%$cosG6#9$F0F-*&\"\"'F0-%$sinGF5F0F0-F46#,$*&F/F0 F6F0F0F0*&F,F0-F:F " 0 "" {MPLTEXT 1 0 373 "Fou r:=proc(N,f)\nlocal x,a,b,n,i,xxx,M;\na:=(f,n)->1/Pi*evalf(Int(f(x)*co s(n*x),x=-Pi..Pi));\nb:=(f,n)->1/Pi*evalf(Int(f(x)*sin(n*x),x=-Pi..Pi) );\nif N mod 2 = 1 then\n M:=(N-1)/2;\n xxx:=a(f,0)/2+sum(a(f,i) *cos(i*x)+b(f,i)*sin(i*x),i=1..M);\n else\n M:=(N-2)/2;\n xxx:= a(f,0)/2+sum(a(f,i)*cos(i*x)+b(f,i)*sin(i*x),i=1..M)+a(f,N/2)*cos(N/2* x);\n fi;\nunapply(xxx,x)\nend;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%FourGj+6$%\"NG%\"fG6)%\"xG%\"aG %\"bG%\"nG%\"iG%$xxxG%\"MG6\"F1C&>8%j+6$F(F-F16$%)operatorG%&arrowGF1* &%#PiG!\"\"-%&evalfG6#-%$IntG6$*&-9$6#T#\"\"\"-%$cosG6#*&9%FHFGFHFH/FG ;,$F;F8&j+F6F1F7F1*&F;F<-F>6#-FA6$*&FDFH-%$si nGFKFHFNFHF1F1FQ6$FTFT@%/-%$modG6$FE\"\"#FHC$>8*,&*&#FHF`oFHFEFHFH#FHF `oF<>8),&*&FfoFH-F46$FMFTFHFH-%$sumG6$,&*&-F46$FM8(FH-FJ6#*&FepFHFRFHF HFH*&-FVFdpFH-FinFgpFHFH/Fep;FHFcoFHC$>Fco,&*&FfoFHFEFHFHFHF<>Fio,(*&F foFHF\\pFHFHF^pFH*&-F46$FM,$*&FfoFHFEFHFHFH-FJ6#,$*&FfoFH*&FEFHFRFHFHF HFHFH-%(unapplyG6$FioFRF1F1F16$FTFT" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Four(5,exp)(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,, *&$\"+OR([:\"!\")\"\"\"%#PiG!\"\"F(*&$\"+8z2wO!\"*F(-%$cosG6#%\"zGF(F* *&$\"+5z2wOF.F(-%$sinGF1F(F(*&$\"+n6Vq9F.F(-F06#,$*&$\"\"#\"\"!F(F2F(F (F(F(*&$\"+GB'3%HF.F(-F7F " 0 "" {MPLTEXT 1 0 57 "plot(\{seq(Four(i,exp)(x),i=1..2),exp(x)\},x=-Pi-1..Pi+.5);" } }{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6'-%'CURVESG6$7jn 7$$!3N++JYEfTT!#<$\"3i(pkdIrAm&F*7$$!3s(o*\\c8%>(RF*$\"3u2Q&3rFg:'F*7$ $!3H_iNw'GV#QF*$\"3Reb*4#3;GlF*7$$!3E$o1#zFKeOF*$\"31+w)zT/A(oF*7$$!3Q VC@([;7\\$F*$\"3VGV$>6f(HrF*7$$!3YKb4J)34$F*$\"3U!H]aRIuM(F*7$$!3\"pc(ypV06I F*$\"3S\"zO(F*7$$!3iZ-I>zM\"o#F*$\"3mLip-sjppF*7$$!30oPFg%[?^#F*$\"3 cpBLPoVZmF*7$$!3/G;h/%HHO#F*$\"3qN>*[/0HH'F*7$$!35L$)omm0&>#F*$\"38!\\ xiVNZ#eF*7$$!3+XU *H(QZF*7$$!3vi*pr4Ulr\"F*$\"3O\"QEG$f&*4UF*7$$!3f9LjLj8T:F*$\"33=b3^91 nNF*7$$!3;#*e!RkWDR\"F*$\"3<*4^wOvU-$F*7$$!3%*z\"*=%=(p>7F*$\"39@uQ]Sw 6CF*7$$!3!>&\\Y%*ypm5F*$\"3]9Q6@`Y+>F*7$$!3wq`aXUL))*)!#=$\"3MSMfcNj(Q \"F*7$$!3A(f1r_n)*Q(F]s$\"3iLk)*ox**)e*F]s7$$!3i\"3'e'>N?s&F]s$\"3wk,K *HIc&eF]s7$$!3g^BEwWW!>%F]s$\"3qMvy`-h!=$F]s7$$!3o7\"o\\sIWO$F]s$\"3)y *4Isr*41#F]s7$$!3wtQntpTQDF]s$\"3#oBiJn0!y6F]s7$$!3Y7$$!3\\6cbBpCC#)F^u$\"3$e@j.J6!y9F]s$ \"3wmV-;S#z+%F^u7$$\"3!*Qbs()4n%G#F]s$\"3#y]b'R@R_&*F^u7$$\"3S]q9m$H!= JF]s$\"3%H&**)fZIDx\"F]s7$$\"3!>coXu(Q^RF]s$\"38,)\\vppE$GF]s7$$\"3iyI 9D\\%>e&F]s$\"3]xb9#4;)zbF]s7$$\"3ocq.RGffrF]s$\"38r*o#Rd4E!*F]s7$$\"3 e_/\"e'=I6*)F]s$\"3_(o)\\/-al8F*7$$\"3!GFxO.H&[5F*$\"3())Ri/YzA%=F*7$$ \"3h?P1**ee;7F*$\"3#)\\nu\"fI5S#F*7$$\"3!*3`E(Rq)o8F*$\"3TZZR!f;)QHF*7 $$\"3CbmSxvNN:F*$\"3%z)*pYdHea$F*7$$\"3?=.FR!4?p\"F*$\"3?gGu`\\d?TF*7$ $\"3Wt[)R&\\vb=F*$\"3a:d-_')[4ZF*7$$\"3K7mk:l%e,#F*$\"3UA2tW6ke_F*7$$ \"3Y6F>WvW$=#F*$\"3E'yWMFk**y&F*7$$\"3Lct`as'[M#F*$\"3;<_-=w%eC'F*7$$ \"3.1,tAA%*4DF*$\"3=+^%[`rGk'F*7$$\"3;n;%oG]On#F*$\"3e%[[A5rp&pF*7$$\" 3!RP)p&*43CGF*$\"3!HPt_!zSorF*7$$\"3ng;#*ziG5HF*$\"3%*H5LhNDasF*7$$\"3 WZ\\9k:\\'*HF*$\"3mm/2,]_8tF*7$$\"3k3\\,)f%ftIF*$\"3_3m^!\\gOM(F*7$$\" 3%)p[)=j(p]JF*$\"3_a9'*[M+_tF*7$$\"3\"\\gRva0HB$F*$\"3+3_d<3%oL(F*7$$ \"3(*RV>jM6:LF*$\"33A*>F;_pH(F*7$$\"3_-'pz#pz$R$F*$\"3$**>Ig2ieB(F*7$$ \"35l[u#R![sMF*$\"3UuZq@Wu_rF*7$$\"3@++&*\\EfTOF*$\"3*o;C()yR@!pF*-%'C OLOURG6&%$RGBG$\"#5!\"\"$\"\"!Fd_lFc_l-F$6$7W7$F($\"3m^Nu@7v*e\"F^u7$F .$\"3-TqdhGo$)=F^u7$F3$\"3U<,.o(3L=#F^u7$F8$\"3+\"ooX!3dxDF^u7$F=$\"3a *pK43zj/$F^u7$FG$\"3%=<***3df(f$F^u7$FQ$\"3#y*o-M3P(>%F^u7$Fen$\"3e5\")F^u7$F^p$\"3igAJ*G.WT*F^u7$Fcp$\"3.P!GO^AN6\"F]s7$Fhp$\"3yLvg *3nzJ\"F]s7$F]q$\"3'4@vWJG/b\"F]s7$Fbq$\"3aqMTIT'oz\"F]s7$Fgq$\"3M&3*G 8jPT@F]s7$F\\r$\"3wM$)*R-BW[#F]s7$Far$\"3uynB3e>`HF]s7$Ffr$\"360=o)RI9 W$F]s7$F[s$\"3O]5!oIU/2%F]s7$Fas$\"3%=tY!\\f(fx%F]s7$Ffs$\"3[**4CUm!Gk &F]s7$F[t$\"3E-CFD'\\nd'F]s7$Fet$\"3u*f1#eg9exF]s7$F`u$\"36v*zm0'[5#*F ]s7$F\\v$\"3i#=[u,S%p5F*7$Ffv$\"3ebXRy@nc7F*7$F`w$\"3?J[#)*>!f%[\"F*7$ Few$\"3%G_Y(*\\9vu\"F*7$Fjw$\"3s3j\\y&[h/#F*7$F_x$\"3L8H&zN$)yV#F*7$Fd x$\"3)R#3g*p]M&GF*7$Fix$\"3)\\kO5DVcP$F*7$F^y$\"3zDhPAy!4$RF*7$Fcy$\"3 nK%f)fa)Hk%F*7$Fhy$\"3yS(z\"*fz.V&F*7$F]z$\"3MHcj5b_'R'F*7$Fbz$\"3%R+> Dbzq](F*7$Fgz$\"3?:FhAp&o())F*7$F\\[l$\"3w&R&)\\y)=V5!#;7$Fa[l$\"3:7$y N\">UI7Fcgl7$Ff[l$\"3!)foGavF\\9Fcgl7$F[\\l$\"3Wj^I#oXXo\"Fcgl7$Fe\\l$ \"3Te+&y:>:+#Fcgl7$Fj\\l$\"3gI;#Fcgl7$F_]l$\"3B1+PC]BNBFcgl7$Fd ]l$\"3[tUv-:KNDFcgl7$Fi]l$\"3[us/%p^Dv#Fcgl7$F^^l$\"3OE(>ne!)y(HFcgl7$ Fc^l$\"3#=ubFJb;A$Fcgl7$$\"3'GVZ8_Oqb$F*$\"3W69Q,Y\"f]$Fcgl7$Fh^l$\"3/ `HN-_D:QFcgl-F]_l6&F__lFc_lF`_lFc_l-F$6$7S7$F($\"33kyC6z2wOF*7$F.F`jl7 $F3F`jl7$F8F`jl7$F=F`jl7$FGF`jl7$FQF`jl7$FenF`jl7$F_oF`jl7$FdoF`jl7$Fi oF`jl7$F^pF`jl7$FcpF`jl7$FhpF`jl7$F]qF`jl7$FbqF`jl7$FgqF`jl7$F\\rF`jl7 $FarF`jl7$FfrF`jl7$F[sF`jl7$FasF`jl7$FfsF`jl7$F[tF`jl7$FetF`jl7$F`uF`j l7$F\\vF`jl7$FfvF`jl7$F`wF`jl7$FewF`jl7$FjwF`jl7$F_xF`jl7$FdxF`jl7$Fix F`jl7$F^yF`jl7$FcyF`jl7$FhyF`jl7$F]zF`jl7$FbzF`jl7$FgzF`jl7$F\\[lF`jl7 $Fa[lF`jl7$Ff[lF`jl7$F[\\lF`jl7$Fe\\lF`jl7$F_]lF`jl7$Fi]lF`jl7$Fc^lF`j l7$Fh^lF`jl-F]_l6&F__lF`_lF`_lFc_l-%+AXESLABELSG6$Q\"x6\"Q!Fh]m-%%VIEW G6$;$!+aEfTT!\"*$\"+aEfTOF`^m%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Q:=i->(ceil(i)-i)*Four(floor (i),exp)(x)+(ceil(i)-i+1)*Four(ceil(i),exp)(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QGj+6#%\"iG6\"6$%)operatorG%&arrowGF(,&*&,&-%%ceilG 6#9$\"\"\"F2!\"\"F3--%%FourG6$-%&floorGF1%$expG6#%\"xGF3F3*&,(F/F3F2F4 F3F3F3--F76$F/F;F " 0 "" {MPLTEXT 1 0 5 "Q(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&$\"+OR([: \"!\")\"\"\"%#PiG!\"\"F(*($\"+OR([:\"F'F(F)F*-%$cosG6#%\"xGF(F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "with(plots):\nanimate( plot, [Q(i),x=-Pi-1..Pi+.5], i=1..2);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot3d(Q(i),x=-Pi-1..Pi+.5,i=1..3);" }}{PARA 7 "" 1 " " {TEXT -1 33 "Warning, computation interrupted\n" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 3 "Q\}]" }}}}{MARK "7 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }