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{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 10 "Chapter
 5." }}{PARA 4 "" 0 "" {TEXT -1 75 "An Introduction to the Mathematics
 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 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "
Section 5.3" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 9 "Page 146." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(lina
lg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "el:=matrix(7,7);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 7 do\n\011
for j from 1 to 7 do\n\011\011el[i,j]:= 0:\n\011od  od:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "el[1,5]:=2/25:  el[1,6]:=7/25: el[
1,7]:=21/50:\n  el[2,1]:=657/1000: el[3,2]:=93/100: el[4,3]:=93/100: e
l[5,4]:=93/100:\n  el[6,5]:=935/1000: el[7,6]:=935/1000:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "evalm(el &* [P0,P1,P2,P3,P4,P5,P6])
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "el10:=evalf(evalm(el^1
0)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Digits:=2;\n  evalf
(evalm(el10));\n  Digits:=10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "fel:=evalf(evalm(el));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "vel:=eigenvects(fel);" }}}{PARA 0 "" 0 "" {TEXT -1 24 "We list t
he eigenvalues." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "eigens:=[
seq(vel[i][1],i=1..7)];" }}}{PARA 0 "" 0 "" {TEXT -1 174 "We extract t
he eigenvector associated with the largest real eignevalue. This large
st can be found with sort. Then, count which eigenvalue this is among \+
the above list called " }{TEXT 256 6 "eigens" }{TEXT -1 1 "." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ordeig:=sort(eigens);" }}}
{PARA 0 "" 0 "" {TEXT -1 225 "We choose vec[n][3][1], where n is the t
he eigenvalue which is real and largest. When composing this code, thi
s largest was the sixth eigenvalue. It may be different when you run t
he code. Here is a way to let Maple choose n." }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 61 "for j from 1 to 7 do\nif eigens[j]=ordeig[1] the
n n:=j fi;\nod;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "n;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "lambda:=vel[n][1]; vec:=vel[
n][3][1];" }}}{PARA 0 "" 0 "" {TEXT -1 46 "We check to see that what w
e have is a vector." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "type(
vec,vector);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "V:=[seq(vec
[i]/vec[1],i=1..7)];" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 8 "Page 148" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 238 "chk:=[1,el[2,1]/lambda, el[2,1]*el
[3,2]/lambda^2,\n\011el[2,1]*el[3,2]*el[4,3]/lambda^3,\n\011el[2,1]*el
[3,2]*el[4,3]*el[5,4]/lambda^4,\n\011el[2,1]*el[3,2]*el[4,3]*el[5,4]*e
l[6,5]/lambda^5,\n\011el[2,1]*el[3,2]*el[4,3]*el[5,4]*el[6,5]*el[7,6]/
lambda^6];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "evalf(evalm(e
l10&*[1,1,1,1,1,1,1]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "
evalm(lambda^10*V);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 8 "Page 151" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "P:=(y,t)->h(y-t)*exp(-int(mu(y-t+u,
u),u=0..t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "diff(P(y,t)
,t)+diff(P(y,t),y)+mu(y,t)*P(y,t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" 
{TEXT -1 9 "Exercises" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 11 "Exercise 1." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "P0:=t->(100-t)*(25+t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
24 "sum('P0(p)','p'=0..100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 39 "birth0:=1.9*sum('P0(p)','p'=21..30)/10;" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "plot(P0(t),t=0..100);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 30 "Death:=t->exp(.0756*t-1.6134);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 144 "P1:=proc(p) if p <= 1 then birth0 else\n
\011\011\011  if 1 < p and p < 100 then P0(p-1)*(1-Death(p-1)/1000) el
se\n\011\011\011  if p = 100 then 0\n\011\011\011  fi fi fi end;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sum('P1(p)','p'=0..100);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "birth1:=1.9*sum('P1(p)','p'
=21..30)/20;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(P1,2..
100);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "P2:=proc(p) if p <= 1 t
hen birth1 else\n\011\011\011  if 1 < p and p < 100 then P1(p-1)*(1-De
ath(p-1)/1000) else\n\011\011\011  if p = 100 then 0\n\011\011\011  fi
 fi fi end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sum('P2(p)',
'p'=0..100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "birth2:=1.9
*sum('P2(p)','p'=21..30)/20;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 16 "plot(P2,3..100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0" 0 }
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