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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 98 "   This worksheet shows you how
 to create a function and plot discrete iterates from the function." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "    Lets
 create the function " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 
0 "" {TEXT -1 10 "          " }{XPPEDIT 18 0 "f(P) = lambda*P;" "6#/-%
\"fG6#%\"PG*&%'lambdaG\"\"\"F'F*" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "    which comes from the \+
discrete population dynamics equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 9 "         " }{XPPEDIT 18 0 "P[t+1] = la
mbda*P[t];" "6#/&%\"PG6#,&%\"tG\"\"\"F)F)*&%'lambdaGF)&F%6#F(F)" }
{TEXT -1 4 " ,  " }{XPPEDIT 18 0 "P[0] = A;" "6#/&%\"PG6#\"\"!%\"AG" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 25 "     Lets create f first." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f := P \+
-> lambda*P;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "  Now let
s consider some examples." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "P[1] := f(P[0]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "P[2] := f(P[1]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 15 "   Lets define " }{XPPEDIT 18 0 "lambda;" "6#%'lam
bdaG" }{TEXT -1 6 "  and " }{XPPEDIT 18 0 "P;" "6#%\"PG" }{TEXT -1 1 "
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 29 "lambda := 1.025; P[0] := 250;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "   Lets look at " }{XPPEDIT 18 
0 "f(P);" "6#-%\"fG6#%\"PG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "f(P);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 20 "  Lets graph this f." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 19 "plot(f(P),P=0..10);" }}}{EXCHG {PARA 0 "> " 
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-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "  Now lets let Maple generate s
ome data." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "N := 1
0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "for t from 0 by 1 to \+
N do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "  P[t+1] := f(P[t]);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 27 "   Now lets plot this data." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 29 "listplot([seq(P[t],t=0..N)]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 123 "   If you click on the above graph with the left \+
button and then with the right button you can do a point plot under St
yle." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 0 0" 8 }{VIEWOPTS 
1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }