{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 98 "This file contains the Map le commands demonstrated in the lecture on January 24, without comment s:" }{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "with(plots): with(DEtools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f1 := x *(r - exp(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "df1 := di ff(f1,x);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(\{f1=0,df1=0\},\{x,r\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "r := 0.5: plot(f1,x=-1..0.5);" }}{PARA 13 "" 1 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "r := 'r':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f2 := (x,r) -> r - x - exp(-x);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "df2 := unapply(diff(f2(x,r), x),x,r);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "solve(\{f2(x,r) =0,df2(x,r)=0\},\{x,r\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalf(f2(2,2),100);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sn2 := solve(f2(x,r)=0,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(sn2,r=0..4);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "logeq := diff(N(t),t) = r*N(t)*(1-N(t)/K);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "loginit := N(0) = N0;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "logsoln := dsolve(\{logeq,lo ginit\},N(t));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "r := 1; K := 4; N0 := 0.2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(rhs(logsoln),t=0..20);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dfieldplot(logeq,N(t),t=0..1 0,N=-2..6,arrows=SLIM);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "DEplot(logeq,N(t),t=0..20,N=-2..6);" }{TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "DEplot(logeq,N(t),t=0..10, N=-2..6,[[N(0)=1]],stepsize=0.1,linecolor=black);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "iniset := [seq([N(0)=i],i=-1 ..5)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "DEplot(logeq,N(t) ,t=0..10,N=-2..6,iniset,stepsize=0.1,linecolor=black);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Get help:\n" }{MPLTEXT 1 0 7 "?DEplot" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 98 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }