{VERSION 4 0 "IBM INTEL NT" "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 "" 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading
 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 
0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 
1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 0 "" 0 "" {TEXT -1 31 "This is all the Maple syntax in" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 11 "Chapter
 11." }}{PARA 4 "" 0 "" {TEXT -1 75 "An Introduction to the Mathematic
s of Biology, with Computer Algebra Models" }}{PARA 4 "" 0 "" {TEXT 
-1 34 "by Yeargers, Shonkwiler, & Herod. " }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "The Syntax is written for Maple 6.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 11 "Exercise 2." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "x:=(p+q/2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 21 "y:=2*(p+1/2)*(r+q/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 9 "z:=1-x-y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "X:=(x+y/2
)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "simplify(X);  simpl
ify(x);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
11 "Exercise 3." }}{PARA 0 "" 0 "" {TEXT -1 6 "part a" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 53 "u:=(2*pA*pa)^2*(1/4)+2*(2*pA*pa)*(pa^2)*1
/2+(pa^2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "pA:=1-pa;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "aaxaa:=simplify((pa^2)^2/u
);" }}}{PARA 0 "" 0 "" {TEXT -1 6 "part b" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "plot(aaxaa,pa=0.001..0.25);" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 11 "Exercise 4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "T:=matrix(2,2,[0,1,1/2,1/2]);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "v:=vector([0.1,0.3]);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 15 "w:=evalm(T&*v);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "v:=evalm(T&*w);" }}}{PARA 0 "" 0 "" {TEXT -1 47 "Here
 is a loop that will compute ten multiples." }{TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "doten:=proc(V)\n  local i,x,y:\ny:
=v;\nfor i from 1 to 10 do\n   x:=y:\n   y:=evalm(T&*x):\nod:\neval(y)
;\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "v:=vector([0.1,0
.3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "w:=doten(v);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "v:=doten(w);" }}}{PARA 0 "" 
0 "" {TEXT -1 9 "The ratio" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
10 "v[1]/v[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "v:=[1,1];
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(T&*v);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(T);" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Exercise 6." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "F:=x->c*x+(1
-c)*p^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "x=0: y:=F(x); w
:=F(y); simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}}{MARK "0 0" 31 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 
2 33 1 1 }