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{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
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{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "This maple worksheet prod
uce Fourier sine expansions, plots, and approximations of functions on
 [0,1]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "input the number N of terms in th
e partial sums (use some number <20 to avoid long computations)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "N:=10;" }}{PARA 11 "" 0 "" 
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"#5" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 24 "input the function  f(x)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f:=x->x;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&arrowGF(9$F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "generate  and diaply the Fourier s
ine coefficients. of  f  up to N " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "b:=array(1..N);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 
"for n to N do b[n]:=2*int(sin(n*Pi*x)*f(x),x=0..1) od:" }}{PARA 11 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for n to N d
o b[n] od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%&arrayG6$;\"\"\"
\"#57\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%#PiG!\"\"\"\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%#PiG!\"\"F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*$%#PiG!\"\"#\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,$*$%#PiG!\"\"#F&\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%#
PiG!\"\"#\"\"#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%#PiG!\"\"#
F&\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%#PiG!\"\"#\"\"#\"\"(" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%#PiG!\"\"#F&\"\"%" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,$*$%#PiG!\"\"#\"\"#\"\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*$%#PiG!\"\"#F&\"\"&" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 35 "generate the partial sums of  f(x) " }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 40 "sf:=x->sum('b[j]*sin(j*Pi*x)','j'=1..N);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sfG:6#%\"xG6\"6$%)operatorG%&arrowG
F(-%$sumG6$.*&&%\"bG6#%\"jG\"\"\"-%$sinG6#*(F4F5%#PiGF59$F5F5/.F4;F5%
\"NGF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "plot  f  and its part
ial Fourier sine sum up to N" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 43 "plot(f(x),x=0..1,title=`f(x)`,thickness=2);" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 62 "plot(sf(x),x=0..1, title=`Fourier approximation`,th
ickness=2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "plot([f(x),sf(x)],x=
0..1,title=`f and Fourier sine approxiamtion`,thickness=2);" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "compute
 f its partial sum and their diference at a given point x0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x0:=.6;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "evalf(f(x0));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "e
valf(sf(x0));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalf(f(x0)-sf(x0)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x0G$\"\"'!\"\"" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"\"'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
\"+*)z!yc&!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*6?>K%!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot(sf(x),x=-5..5,title=`Pe
riodic extension`,thickness=2);" }}}}{MARK "14 0 0" 0 }{VIEWOPTS 1 1 
0 1 1 1803 }