{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 0 "" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 50 "Extending of Fourier series onto general interval:" }} }{EXCHG {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 373 "Four:=proc(N,f)\nlocal x,a,b,n,i,xxx,M;\na:= (f,n)->1/Pi*evalf(Int(f(x)*cos(n*x),x=-Pi..Pi));\nb:=(f,n)->1/Pi*evalf (Int(f(x)*sin(n*x),x=-Pi..Pi));\nif N mod 2 = 1 then\n M:=(N-1)/2; \n xxx:=a(f,0)/2+sum(a(f,i)*cos(i*x)+b(f,i)*sin(i*x),i=1..M);\n el se\n M:=(N-2)/2;\n xxx:=a(f,0)/2+sum(a(f,i)*cos(i*x)+b(f,i)*sin( i*x),i=1..M)+a(f,N/2)*cos(N/2*x);\n fi;\nunapply(xxx,x)\nend;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%%FourGj+6$%\"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+F 6F1F7F1*&F;F<-F>6#-FA6$*&FDFH-%$sinGFKFHFNFHF1F1FQ6$FTFT@%/-%$modG6$FE \"\"#FHC$>8*,&*&#FHF`oFHFEFHFH#FHF`oF<>8),&*&FfoFH-F46$FMFTFHFH-%$sumG 6$,&*&-F46$FM8(FH-FJ6#*&FepFHFRFHFHFH*&-FVFdpFH-FinFgpFHFH/Fep;FHFcoFH C$>Fco,&*&FfoFHFEFHFHFHF<>Fio,(*&FfoFHF\\pFHFHF^pFH*&-F46$FM,$*&FfoFHF EFHFHFH-FJ6#,$*&FfoFH*&FEFHFRFHFHFHFHFH-%(unapplyG6$FioFRF1F1F16$FTFT " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "If wont to interpolate function on general interval " }{XPPEDIT 18 0 "`<,>`(alpha,beta);" "6#-%$<,>G6$%&alphaG6#%%betaG" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "transformation \+ of interval " }{XPPEDIT 18 0 "`<,>`(alpha,beta);" "6#-%$<,>G6$%&alphaG %%betaG" }{TEXT -1 15 " onto interval " }{XPPEDIT 18 0 "`<,>`(-Pi,Pi); " "6#-%$<,>G6$,$%#PiG!\"\"F'" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "t[1]:=x->p*x+q;alpha:='alpha';beta:='beta';" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"tG6#\"\"\"j+6#%\"xG6\"6$%)operato rG%&arrowGF+,&*&%\"pGF'9$F'F'%\"qGF'F+F+F+6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%betaG F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "params:=solve(\{t[1]( alpha)=-Pi,t[1](beta)=Pi\},\{p,q\});" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%'paramsG<$/%\"qG,$*(%#PiG\"\"\",&%%betaGF+%&alphaGF+F+,&F.!\"\"F-F +F0F0/%\"pG,$*(\"\"#F+F/F0F*F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "t[1]:=unapply(subs(params,t[1](x)),x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>&%\"tG6#\"\"\"j+6#%\"xG6\"6$%)operatorG%&arrowG F+,&**\"\"#F',&%&alphaG!\"\"%%betaGF'F4%#PiGF'9$F'F'*(F6F',&F5F'F3F'F' F2F4F4F+F+F+6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "t[1] (alpha);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&**\"\"#\"\"\",&%&alphaG! \"\"%%betaGF&F)%#PiGF&F(F&F&*(F+F&,&F*F&F(F&F&F'F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "inverse transformation:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 36 "t[2]:=unapply(solve(t[1](x)=y,x),y);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "simplify((t[1]@t[2])(x));simplify((t[2]@t [1])(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"tG6#\"\"#j+6#%\"yG6 \"6$%)operatorG%&arrowGF+,$*&#\"\"\"F'F2*&,**&%#PiGF2%%betaGF2F2*&F6F2 %&alphaGF2F2*&9$F2F9F2!\"\"*&F;F2F7F2F2F2F6F " 0 "" {MPLTEXT 1 0 49 "al pha:=1;beta:=10;\nxxx:=(Four(25,exp@t[2])@t[1]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG\"\"\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%betaG\"#5" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$xxxG-%\"@G6$j+6#%\"xG6\"6$%)operatorG%&arrowGF+,T*&$ \"+l(Q*QE!\"(\"\"\"-%$cosG6#,$*&$\"\"'\"\"!F49$F4F4F4F4*&$\"+8c!oE'F3F 4-%$sinG6#,$*&$\"#6FFKF4-FB6#,$*&$\"\"$FF3F4-F6FdoF4FN*&$\"+S;Hf;FKF4-F6FapF4F 4*&$\"+b\"Qxo(FKF4%#PiGFNF4*&$\"+tgR06FKF4-FBF7F4FN*&$\"+-Ut&H\"FKF4-F B6#,$*&$\"\"&F5+'3*F3F4-F6F[oF4FN*&$\"+'3jrH#FKF4-FBFMF4F4*&$\"+1^R`:FKF 4-FBFcrF4FN*&$\"+MytR)*FRF4-F66#,$*&$\"#5F%o]F\"&%\"tG6#F4" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot(\{exp(x),xxx(x),_Four(5 ,exp)(x)\},x=-Pi..10);" }}{PARA 7 "" 1 "" {TEXT -1 161 "Warning, unabl e to evaluate 1 of the 3 functions to 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