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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 682 "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  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;\nFourier:=(f,N,alpha,beta)->Four(N,f@(
x->t[2](x,alpha,beta)))@(x->t[1](x,alpha,beta));\nt[1] := proc (x, alp
ha, beta) options operator, arrow; 2/(-alpha+beta)*Pi*x-Pi*(beta+alpha
)/(-alpha+beta) end proc;\nt[2] := proc (x, alpha, beta) options opera
tor, arrow; 1/2*(Pi*beta+Pi*alpha-x*alpha+x*beta)/Pi end proc;\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 ";\n" }}{PARA 12 "" 1 "" {XPPMATH 20 
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\"tG6#\"\"\"j+6%%\"xG%&alphaG%%betaG6\"6$%)operatorG%&arrowGF-,&**\"\"
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f(x),x=(a+b)/2,N);\ng[2]:=Fourier(f,N,a,b);\nprint([seq(a+(b-a)/N*i,i=
0..N)], [seq(F(x[i+1]),i=0..N)]);\ng[3]:=interp([seq(a+(b-a)/N*i,i=0..
N)], [seq(f(a+(b-a)/N*i),i=0..N)], z);\n[unapply(g[1],x),g[2],unapply(
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "for i from 1 to 3 do\ni,evalf(Int(s
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20 "6$\"\"\"$\"+)y7pw\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#$
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" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Nejpresnejsi je aproximce Fou
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f:=exp@sin@ln;\na:=-10;b:=20
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG!#5" }}{PARA 11 "" 1 "" 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plot(\{seq(F[i](z),i=2..3),\nsin(si
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#?" }}{PARA 11 "" 1 "" 
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