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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 39 "Using Maple to Calculate Fourie
r Series" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 75 "Here is a Maple procedure for calculating the Fourie
r series of a function " }{XPPEDIT 18 0 "f(x);" "6#-%\"fG6#%\"xG" }
{TEXT -1 22 " on the interval from " }{XPPEDIT 18 0 "-L;" "6#,$%\"LG!
\"\"" }{TEXT -1 4 " to " }{XPPEDIT 18 0 "L;" "6#%\"LG" }{TEXT -1 1 ".
" }}{PARA 0 "" 0 "" {TEXT -1 37 "(Actually, it is several procedures.)
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "assume(n
,integer):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "a := proc(n)
\n   integrate(f(x)*cos(n*Pi*x/L),x=-L..L)/L\n end;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 62 "b := proc(n)\n   integrate(f(x)*sin(n*Pi*
x/L),x=-L..L)/L\n  end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 
"fourier_partial_sum := proc(n)\n   a(0)/2 + sum(a(j)*cos(j*Pi*x/L) + \+
b(j)*sin(j*Pi*x/L),j=1..n)\n end;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 19 "Here is an example." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f := x -> x;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a(n);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "b(n);" }}}{PARA 0 "" 0 "" {TEXT -1 10 "Let
's set " }{XPPEDIT 18 0 "L = 1;" "6#/%\"LG\"\"\"" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
7 "L := 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a(n);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "b(n);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "fourier_partial_sum(5);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 55 "plot(\{x,fourier_partial_sum(2)\},x=-1..1,nump
oints=200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plot(\{x,fou
rier_partial_sum(5)\},x=-1..1,numpoints=200);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 56 "plot(\{x,fourier_partial_sum(10)\},x=-1..1,numpo
ints=200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot(\{x,four
ier_partial_sum(20)\},x=-1..1,numpoints=200);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 57 "plot(\{x,fourier_partial_sum(50)\},x=-1..1,numpo
ints=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f := x -> ab
s(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "L := 'L';" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(L,positive);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a(n);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "b(n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 23 "fourier_partial_sum(5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "L := 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot(\{f(x)
,fourier_partial_sum(2)\},x=-1..1,numpoints=200);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 58 "plot(\{f(x),fourier_partial_sum(5)\},x=-1..1
,numpoints=200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot(\{
f(x),fourier_partial_sum(10)\},x=-1..1,numpoints=200);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f := x -> \npiecewise(x<0,-1,x<1,1)
; \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "L := 1;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a(n);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "b(n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fo
urier_partial_sum(5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "pl
ot(\{f(x),fourier_partial_sum(2)\},x=-1..1,numpoints=200);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot(\{f(x),fourier_partial_sum(5)
\},x=-1..1,numpoints=200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
59 "plot(\{f(x),fourier_partial_sum(10)\},x=-1..1,numpoints=200);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot(\{f(x),fourier_partial_
sum(20)\},x=-1..1,numpoints=200);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "plot(\{f(x),fourier_partial_sum(50)\},x=-1..1,numpoin
ts=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "48
" 0 }{VIEWOPTS 0 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }