{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 23 "Chapter 3, Sections 3.5" }}{PARA 4 "" 0 "" {TEXT -1 75 "An Introduction to th e 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 33 "The Syntax is written f or Maple 6" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Section 3.5" }}{PARA 0 "" 0 "" {TEXT -1 7 "Page 91" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "f0:=t->exp(t/10);\ndsolve(\{ diff(y(t),t)=f0(t-1),y(0)=f0(0)\},y(t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "f1:=unapply(rhs(%),t);\ndsolve(\{diff(y(t),t)=f1(t-1) ,y(1)=f1(1)\},y(t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "f2: =unapply(rhs(%),t);\ndsolve(\{diff(y(t),t)=f2(t-1),y(2)=f2(2)\},y(t)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f3:=unapply(rhs(%),t); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "plot(\{[t,f0(t),t=-1.. 0],[t,f1(t),t=0..1],[t,f2(t),t=1..2],\n [t,f3(t),t=2..3]\},t=-1..3, y =-1..6,color=black);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Page 93" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "xval:=[seq(a[i],i=1..3)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "yval:=[seq(b[i],i=1..3)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "lny:=map(ln,yval);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "with(stats):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "fit[leastsquare[[x,y],y=r*x+ln(A),\{r\}]]([xval,lny]) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "coeff(rhs(%),x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "combine(simplify(%));" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Example 3 .5.1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "tt:=[seq(1790+i*10,i=0..20)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 264 "pop:=[ 3.929214, 5.308483, 7.239881, 9.638453, 12.8660 20, \n\011\011 17.069453, 23.191876, 31.433321, 39.818449, 50.15578 3, \n\011\011 62.947714, 75.994575, 91.972266, 105.710620, 122.775046 ,\n\011\011131.669275, 151.325798,179.323175, 203.302031, 226.545805, \n\011\011248.709873];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "d ata:= [seq([tt[i],pop[i]],i=1..21)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot(data,style=POINT,symbol=CROSS,tickmarks=[4,5]); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "scaledata:= [seq([(i-1) *10,pop[i]],i=1..21)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "p lot(scaledata,style=POINT,symbol=CROSS,tickmarks=[4,5]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "semilnpop:= [seq([(i-1)*10,ln(pop[i ])],i=1..15)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot(semi lnpop,style=POINT,symbol=CIRCLE);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "tzeroed:=[seq((i-1)*10,i=1..15)];\nlnpop:=[seq(ln(pop [i]),i=1..15)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(sta ts):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fit[leastsquare[[t, y],y=m*t+b]]([tzeroed,lnpop]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "y:=unapply(rhs(%),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "J:=plot(exp(y(t-1790)),t=1790..1930,tickmarks=[4,5]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "K:=plot(data,style=POINT,sym bol=CROSS,tickmarks=[4,5]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plots[display](\{J,K\});" }}}{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 2." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "yrs:=([9,19,29,39,49,59,69,79,89]);\nDR:=([.3,1.5, 1.9, 2.9, 6.5, \+ 16.5, 37, 83.5, 181.9]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "pts:=[seq([yrs[i],DR[i]], i=1..9)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot(pts,style=POINT, symbol=CROSS);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "lnpts:=[seq([yrs[i],ln(DR[i]) ], i= 1..9)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(lnpts,style =POINT,symbol=CIRCLE);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "w ith(stats):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "lnDR:=map(ln ,DR);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "fit[leastsquare[[t ,y],y=a*t+b]]([yrs,lnDR]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "a:=op(1,op(1,rhs(%))); b:=op(2,rhs(%%));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "death:=t->exp(a*t+b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "J:=plot(pts,style=POINT, symbol=CROSS):\nK:=plot(d eath(t),t=0..90):\nplots[display](\{J,K\});" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "Exeercise 4." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "AIDS:=([97, 206, 406, 700 , 1289, 1654, 2576, 3392, \n\0114922, 6343, 8359, 9968,12990,14397, 16 604, 17124, \n\01119585, 19707, 21392, 20846, 23690, 24610,26228, \n \01122768, 4903]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "CAC:= [seq(sum(AIDS[j]/1000.0,j=1..i),i=1..24)];" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 34 "Time:=[seq(1981+(i-1)/2,i=1..24)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "pts:=[seq([Time[i],CAC[i]],i=1..24) ]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "LnCAC:=map(ln,CAC);\n Times:=[seq((i+1)/2/10,i=1..24)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "with(stats):\nfit[leastsquare[[x,y],y=m*x+b]]([Times, LnCAC]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "k:=op(1,op(1,rh s(%))); A:=op(2,rhs(%%));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y:=t->exp(A)*exp(k*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "J:=plot(y((t-1980)/10),t=1980..1992):\nK:=plot(pts,style=POINT,sy mbol=CIRCLE):\nplots[display](\{J,K\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{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 }