{VERSION 4 0 "APPLE_PPC_MAC" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 18 0 
0 0 0 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R
3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 0 2 1 2 0 
0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 
257 1 {CSTYLE "" -1 -1 "Courier" 1 18 0 0 0 0 2 2 2 0 0 0 0 0 0 1 }0 
0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 3" -1 258 1 {CSTYLE "
" -1 -1 "Courier" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 4" -1 259 1 {CSTYLE "" -1 -1 "Courier
" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "R3 Font 5" -1 260 1 {CSTYLE "" -1 -1 "Courier" 1 14 0 0 0 0 
1 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 0 "" 0 "" {TEXT -1 62 "MAPLE WORKSHEET:  Guessing the Fo
urier Expansion of a function" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "read(`/hom
e/mathphys/paradigm1/input`):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "
Look at the function f(x) plotted below." }}{PARA 0 "" 0 "" {TEXT -1 
69 "It is a linear combination of sin(nx) for different values of n, i
.e." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 "  \+
   f(x)=b1 sin(x) + b2 sin(2x) + b3 sin(3x) + ...\n" }}{PARA 0 "" 0 "
" {TEXT -1 225 "Your job is to guess the values of the coefficients.  \+
To make your job a little easier, I have put in only 3 nonzero terms, \+
all of the coefficients are positive or negative integers, and I have \+
not included any terms for n>5." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "
plot(f(x),x=0..2*Pi,color=black);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
120 "You might want to start by plotting sin(nx) for various values of
 n if you don't remember what this function looks like:" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 35 "plot(sin(x),x=0..2*Pi,color=black);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 199 "Guess the most important term.  P
lot your guess and the function f(x) on the same graph.\nKeep guessing
 more and more terms until the graph for your guess and the graph for \+
f(x) overlap.  For example:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "mygu
ess:=7*sin(4*x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "The unknown f
unction is BLACK and your guess is RED." }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 51 "plot([f(x), myguess], x=0..2*Pi,color=[black,red]);" }}}}
{MARK "2 0 0" 11 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 
2 33 1 1 }