{VERSION 5 0 "IBM INTEL NT" "5.0" }
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{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{PSTYLE "Normal" 
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{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 
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{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "T
itle" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 
0 0 -1 12 12 0 0 0 0 0 0 19 0 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 15 "Fourierova \235ada" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Int(sin(x),x=0..Pi/4)=int(si
n(x),x=0..Pi/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$-%$sinG6
#%\"xG/F*;\"\"!,$%#PiG#\"\"\"\"\"%,&*$-%%sqrtG6#\"\"#F1#!\"\"F8F1F1" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 389 "fourier:=proc(f,n)\nlocal
 i,N;\nif n mod 2 = 1 then N:=(n+1)/2\n  else\n    N:=n/2; \nfi;\nfor \+
i from 0 to N do\n  a[i]:=evalf(1/Pi*int(f(x)*cos(i*x),x=-Pi..Pi));\n \+
 b[i]:=evalf(1/Pi*int(f(x)*sin(i*x),x=-Pi..Pi));\nod;\ni:='i';\nif n m
od 2 = 1 then\n  unapply(a[0]/2+sum(a[i]*cos(i*x)+b[i]*sin(i*x),i=1..N
-1),x)\nelse\n  unapply(a[0]/2+sum(a[i]*cos(i*x)+b[i]*sin(i*x),i=1..N-
1)+a[N]*cos(N*x),x);\nfi\nend;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}{PARA 7 "" 1 "" {TEXT -1 65 "Warning, `a` is implicitly declared loc
al to procedure `fourier`\n" }}{PARA 7 "" 1 "" {TEXT -1 65 "Warning, `
b` is implicitly declared local to procedure `fourier`\n" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%(fourierGf*6$%\"fG%\"nG6&%\"iG%\"NG%\"aG%\"bG6
\"F.C&@%/-%$modG6$9%\"\"#\"\"\">8%,&F5#F7F6F;F7>F9,$F5F;?(8$\"\"!F7F9%
%trueGC$>&8&6#F?-%&evalfG6#*&%#PiG!\"\"-%$intG6$*&-9$6#%\"xGF7-%$cosG6
#*&F?F7FTF7F7/FT;,$FKFLFKF7>&8'FF-FH6#*&FKFL-FN6$*&FQF7-%$sinGFWF7FYF7
>F?.F?@%F1-%(unapplyG6$,&&FE6#F@F;-%$sumG6$,&*&FDF7FUF7F7*&FgnF7F_oF7F
7/F?;F7,&F9F7F7FLF7FT-Feo6$,(FhoF;FjoF7*&&FE6#F9F7-FV6#*&F9F7FTF7F7F7F
TF.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f:=x->x^2-2^x;\n
\n\nfor i from 1 to 2 do\nprint(i,fourier(f,i));\nod;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*$)9$\"
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$F/!\"\"F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "plot(\{f(
x),fourier(f,15)(x)\},x=-Pi/2..Pi/2);" }}{PARA 13 "" 1 "" {GLPLOT2D 
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 185 "f:=x->abs(x);\nK:=21;\nll:=
t<1,(t)*fourier(f,1);\nfor i from 1 to K do\nll:=ll, t<i+1 ,(1-(t-i))*
fourier(f,i)+(t-i)*fourier(f,i+1);\nprint(i);\nod:\nF:=piecewise(ll):
\nG:=unapply(F,t):\n#subs();" }}{PARA 7 "" 0 "" {TEXT -1 0 "" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"fG%$absG" }}{PARA 11 "" 1 "" {XPPMATH 
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{XPPMATH 20 "6#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}
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Fjp7$F]u$\"3%>\\UL%)zbP*Fjp7$F`u$\"33+&R4+J60\"F*7$Fcu$\"3;E%ou'=cs6F*
7$Ffu$\"3#)))y\\v*))**G\"F*7$Fiu$\"39D`SN8AH9F*7$F\\v$\"3K0hW%fAuc\"F*
7$F_v$\"3BsxYTa&>r\"F*7$Fbv$\"3%*Q![Ewug%=F*7$Fev$\"3)ftmot$Gv>F*7$Fhv
$\"3mInOegu\"4#F*7$F[w$\"3$yDiT>r5@#F*7$F^w$\"30bQ51U:RBF*7$Faw$\"3G-*
pje7,Z#F*7$Fdw$\"3J=#)[AKqKEF*7$Fgw$\"3#3LDN-dxx#F*7$Fjw$\"3fk6#RNBB\"
HF*7$$\"3tX=#4!HbTHF*$\"3Kz![BA1H'HF*7$F]x$\"3G8P-dyZ,IF*7$$\"3;HB\"HM
-#RIF*$\"3^[#[Ii;m,$F*7$$\"3/')[UXCLtIF*$\"3Ar3%Qzxv-$F*7$$\"3#HWPzaiu
5$F*$\"3\\`iC/V@MIF*7$F`xF_y-Fcx6&FexFixFfxFix-%+AXESLABELSG6$Q\"x6\"Q
!Fagl-%%VIEWG6$;$!+aEfTJ!\"*$\"+aEfTJFigl%(DEFAULTG" 1 2 0 1 10 0 2 9 
1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 1025 "Fourier:=proc(f,n,beta)\nlocal i,
N;\nif n mod 2 = 1 then N:=(n+1)/2\n  else\n    N:=n/2; \nfi;\nfor i f
rom 0 to N do\n  a[i]:=evalf(2/beta*evalf(int(f(x)*cos(2*i*Pi*x/beta),
x=0..beta)));\n  b[i]:=evalf(2/beta*evalf(int(f(x)*sin(2*i*Pi*x/beta),
x=0..beta)));\nod;\ni:='i';\nif n mod 2 = 1 then\n  unapply(a[0]/2+sum
(a[i]*cos(2*i*Pi*x)+b[i]*sin(2*i*Pi*xx),i=1..N-1),x)\nelse\n  unapply(
a[0]/2+sum(a[i]*cos(2*i*Pi*x)+b[i]*sin(2*i*Pi*x),i=1..N-1)+a[N]*cos(N*
2*Pi*x),x);\nfi\nend;\n\nAproximace:=proc(X,Y,F) #vstup: pole bodu, po
kle hodnot, pole funkci. Vystup: linearni kombinace zadanych funkci, k
tera nejlepe aproximuje zadane hodnoty.\nglobal MaticeSoustavy,PraveSt
rany;\nlocal i,j,PX,PF,v\n;\nPF:=nops(F);PX:=nops(X);\ni:='i';j:='j';
\nv:=evalf\n([ unapply(F[i],x)(X[j])  $j=1..PX] $i=1..PF);\n\n#print(v
);\nMaticeSoustavy:=\nmatrix(PF,PF,\n[[sum((v[i][k]*v[j][k]),k=1..PX) \+
$j=1..PF] $i=1..PF]\n);\nPraveStrany:=vector([sum(Y[j]*v[i][j],j=1..PX
) $i=1..PF]);\n\nKoeficienty:=linsolve(MaticeSoustavy,PraveStrany):\nu
napply(sum(Koeficienty[i]*F[i],i=1..PF),x);\nend;" }}{PARA 7 "" 1 "" 
{TEXT -1 65 "Warning, `a` is implicitly declared local to procedure `F
ourier`\n" }}{PARA 7 "" 1 "" {TEXT -1 65 "Warning, `b` is implicitly d
eclared local to procedure `Fourier`\n" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%(FourierGf*6%%\"fG%\"nG%%betaG6&%\"iG%\"NG%\"aG%\"bG6\"F/C&@%/
-%$modG6$9%\"\"#\"\"\">8%,&F6#F8F7F<F8>F:,$F6F<?(8$\"\"!F8F:%%trueGC$>
&8&6#F@-%&evalfG6#,$*&9&!\"\"-FI6#-%$intG6$*&-9$6#%\"xGF8-%$cosG6#,$**
F@F8%#PiGF8FXF8FMFNF7F8/FX;FAFMF8F7>&8'FG-FI6#,$*&FMFN-FI6#-FR6$*&FUF8
-%$sinGFenF8FinF8F7>F@.F@@%F2-%(unapplyG6$,&&FF6#FAF<-%$sumG6$,&*&FEF8
-FZ6#,$*(F@F8FhnF8FXF8F7F8F8*&F\\oF8-Fho6#,$*(F@F8FhnF8%#xxGF8F7F8F8/F
@;F8,&F:F8F8FNF8FX-F]p6$,(F`pF<-Fcp6$,&FfpF8*&F\\oF8-FhoFhpF8F8FaqF8*&
&FF6#F:F8-FZ6#,$*(F:F8FhnF8FXF8F7F8F8FXF/F/F/" }}{PARA 7 "" 1 "" 
{TEXT -1 78 "Warning, `Koeficienty` is implicitly declared local to pr
ocedure `Aproximace`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+Aproximac
eGf*6%%\"XG%\"YG%\"FG6(%\"iG%\"jG%#PXG%#PFG%\"vG%,KoeficientyG6\"F1C+>
8'-%%nopsG6#9&>8&-F66#9$>8$.F?>8%.FB>8(-%&evalfG6#-%\"$G6$7#-FJ6$--%(u
napplyG6$&F86#F?%\"xG6#&F=6#FB/FB;\"\"\"F:/F?;FenF4>%/MaticeSoustavyG-
%'matrixG6%F4F47#-FJ6$7#-FJ6$-%$sumG6$*&&&FEFT6#%\"kGFen&&FEFXFioFen/F
joFZ/FBFgnFfn>%,PraveStranyG-%'vectorG6#7#-FJ6$-Fdo6$*&&9%FXFen&FhoFXF
enFYFfn>8)-%)linsolveG6$FinF`p-FQ6$-Fdo6$*&&F^qFTFenFSFenFfnFUF1FaqF1
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Fourier(exp(x),4,1);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"xG6\"6$%)operatorG%&arrowGF&,*
$\"+G=G=<!\"*\"\"\"*&$\"+-m')*[)!#6F.-%$cosG6#,$*&%#PiGF.9$F.\"\"#F.F.
*&$\"+30MM`!#5F.-%$sinGF5F.!\"\"*&$\"+Y\\`i@F2F.-F46#,$F7\"\"%F.F.F&F&
F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "AZ:=Fourier(xxx,2,10)
;\nplot(AZ(x),x=0..30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AZGf*6#%
\"xG6\"6$%)operatorG%&arrowGF(,&$\"+LLLLK!\")\"\"\"*&$\"+O=@85F/F0-%$c
osG6#,$*&%#PiGF09$F0\"\"#F0F0F(F(F(" }}{PARA 13 "" 1 "" {GLPLOT2D 400 
300 300 {PLOTDATA 2 "6%-%'CURVESG6$7geo7$$\"\"!F)$\"3?+++p^aYU!#;7$$\"
3%)***\\iSmp3%!#>$\"3^D(Q=v@L@%F,7$$\"3m****\\7G$R<)F0$\"3nbyB0.$e6%F,
7$$\"3***\\i:gT<-\"!#=$\"3y%fAL3F[/%F,7$$\"3))**\\(=#**3E7F;$\"3W=t&pN
k/'RF,7$$\"3/+v=U#Q/V\"F;$\"3#z3Ev(48kQF,7$$\"3$*****\\ilyM;F;$\"31%4Y
v'GTdPF,7$$\"3\")*\\7G)[8R=F;$\"3EHU&=\"p1UOF,7$$\"3)***\\7.K[V?F;$\"3
?tcEM?**>NF,7$$\"3')*\\PM_JyC#F;$\"3i%Gle$z>$R$F,7$$\"3w***\\P%)z@X#F;
$\"3%yz)e4?xjKF,7$$\"3#**\\iS;Gll#F;$\"3e$Hud(\\%Q8$F,7$$\"33+]P%[w3'G
F;$\"3`-4U/eb0IF,7$$\"3q*\\(o/[AlIF;$\"3YHXj,l,\")GF,7$$\"3')*****\\7t
&pKF;$\"3]ci(*RtFiFF,7$$\"3-+DJX9#RZ$F;$\"33&=@^5$H^EF,7$$\"3i**\\il(p
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3^****\\(ofV!\\F;$\"3ll8Ug.&>A#F,7$$\"3%)**\\7Gj08`F;$\"3ht*oSBf'RAF,7
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F_x$\"3py9R$Hsh?%F,7$$\"37+D1R.k!3\"F_x$\"3[tmCrlC>TF,7$$\"3?vVB:3?;6F
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#F,7$$\"3c7G)[S_GO\"F_x$\"3w=%3Ja+Od#F,7$$\"31+v=U\"[GQ\"F_x$\"3i.@\\@
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k.?F_x$\"3m&QALjziC%F,7$$\"3*)***\\P4sP-#F_x$\"3&4o$3<RENUF,7$$\"3++D
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i!R]8W7#F_x$\"35[qZ#e<C&RF,7$$\"3A+v$fyTX9#F_x$\"3a.El$QSm&QF,7$$\"3G]
(oz1qY;#F_x$\"37IVFCp!4v$F,7$$\"3K+++]$)z%=#F_x$\"3YX'>\\61pj$F,7$$\"3
R]7.Km#\\?#F_x$\"3Vm_*G#*ek^$F,7$$\"3W+D19\\0DAF_x$\"3M7#4aG*[\"R$F,7$
$\"3]]P4'>$=XAF_x$\"3gS`(zP$*RE$F,7$$\"3c+]7y9JlAF_x$\"3S6\\$*Gx+OJF,7
$$\"3i]i:g(RaG#F_x$\"3\"f&4T*ow&4IF,7$$\"3n+v=U!obI#F_x$\"3-hrIy(>n)GF
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F,7$$\"3A+vV)H%fmCF_x$\"3&[KAh\\eBC#F,7$$\"3L++]i3&o]#F_x$\"3AE!3%Q+1@
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BM5noMF,7$$\"3-)o/)*4St!GF_x$\"3]$3Yn!e_!f$F,7$$\"39+]i:FPFGF_x$\"3&>n
Ep2Hnq$F,7$$\"3E7`WJ`SZGF_x$\"3JMvlvAW:QF,7$$\"3%[ils%zVnGF_x$\"3CIAzT
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3(\\#yNr\")[VUF,7$$\"3TD\"GQ())pFIF_x$\"3L!QQ&3$R7B%F,7$$\"37](oa5kx1$
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31@X.uC`EEF,7$$\"3%)**\\Pf\"o2P$F_x$\"36gJJ``=ODF,7$$\"3h*\\7yv8zS$F_x
$\"3=&3RR7S]Q#F,7$$\"3#)***\\iNf]W$F_x$\"3![)f!y'Q*)zAF,7$$\"3#*\\(oa:
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3')fAG'Q]Q=$F,7$$\"3!)*\\i:?b9w$F_x$\"3Z6]tik>1LF,7$$\"3#***\\Pfio!y$F
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\"3<sn@KfwFUF,7$$\"3!)***\\(o5#*\\SF_x$\"3)*eY07-6(>%F,7$$\"39**\\P%=$
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\"3u*\\PMZQX=%F_x$\"3K9TE*4B%QOF,7$$\"3')***\\7`pP?%F_x$\"3QG2NsU_BNF,
7$$\"3)**\\i!*e+IA%F_x$\"3P;,C\"o$R/MF,7$$\"35+](okJAC%F_x$\"37=QGq&oF
G$F,7$$\"3A+vo/FYhUF_x$\"3_5.kgDUgJF,7$$\"3M++]iPp!G%F_x$\"3%pN4hyR\"R
IF,7$$\"3W+DJ?[#**H%F_x$\"3POQmv))o?HF,7$$\"3d+]7ye:>VF_x$\"3YyN3irz1G
F,7$$\"3!)*\\Pf$pQQVF_x$\"3=*z)z#\\D\"*p#F,7$$\"3#****\\P*zhdVF_x$\"31
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\"3V++v=51OYF_x$\"3e$*)et\"fOoDF,7$$\"3w***\\i!)\\fl%F_x$\"3]XN(Q)\\$)
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