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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "# Fourier Series" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "for n from 1 to 5 do f[n]:=sum(sin(
i*x)/i,i=1..n); end; # odd functions" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "plot([seq(f[i],i=1..5)],x=-Pi..Pi);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 51 "g:=piecewise(x<0,(-Pi-x)/2,(Pi-x)/2); #od
d function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(g,x=-Pi.
.Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "int(g*cos(m*x),x=-
Pi..Pi);#odd integrand" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "i
nt(g*sin(m*x),x=-Pi..Pi);#even integrand" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "assume(m>0,m::integer);int(g*sin(m*x),x=-Pi..Pi);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int(a*sin(m*x)*sin(m*x),x=-
Pi..Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "assume(m1>0,m1:
:integer);int(a1*sin(m1*x)*sin(m*x),x=-Pi..Pi);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 86 "display(plot(g,x=-Pi..Pi,color=black,thickness
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