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\"*$\"+3`=$G'Febl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 13 "" 1 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "We compute first few co
efficients of Fourier series:" }{MPLTEXT 1 0 37 "\na:='a';b:='b';\nfor
 n from 0 to 5 do\n" }{TEXT -1 35 "for algebraical computation we use:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "\n   #a[n]:=1/Pi*int(f*cos(n*x)
,x=-Pi..Pi); \n   #b[n]:=1/Pi*int(f*sin(n*x),x=-Pi..Pi);\n\n" }{TEXT 
-1 107 "for numerial computation we use intert form of function int, a
nd function evalf, with numericaly evaluates." }{MPLTEXT 1 0 101 "\n  \+
 a[n]:=evalf(1/Pi*Int(f*cos(n*x),x=-Pi..Pi));\n   b[n]:=evalf(1/Pi*Int
(f*sin(n*x),x=-Pi..Pi));\n\nod:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"aGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 15 "Then we sum it:" }{MPLTEXT 1 0 61 "\nn:='n';\nphi
:=a[0]/2+sum(a[n]*cos(n*x)+b[n]*sin(n*x),n=1..5);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"nGF$" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiG,8$
\"+vlaa`!#5\"\"\"*&$\"+0>*oa%F(F)-%$cosG6#%\"xGF)!\"\"*&$\"+********>!
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mmmF(F)-F7FIF)F)*&$\"+8Uz=AFGF)-F.6#,$*&\"\"%F)F0F)F)F)F)*&$\"+*******
*\\F(F)-F7FUF)F1*&$\"+oh^0?FGF)-F.6#,$*&\"\"&F)F0F)F)F)F)*&$\"+)******
*RF(F)-F7F[oF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(\{
f,F(x),phi\n\},x=-Pi-1..2*Pi);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 
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:=(f,N)-> unapply(a(f,0)/2+sum(a(f,i)*cos(i*x)+b(f,i)*sin(i*x),i=1..N)
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