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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 41 "Discrete and Continuous \+
Dynamical Systems" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 129 "The cell below shows how Maple can be used to work with \+
the discrete dynamical system used as an example in the browser window
.  " }{TEXT 256 15 "Evaluate it now" }{TEXT -1 1 "." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 402 "k := 0.0
002:\nInitialValue := 0.50:\nDemand := p -> 1000 - 500 * p:\nSupply :=
 p -> 1000 * p - 400:\nfcn := p -> p + k * (Demand(p) - Supply(p)):\n
\nprice :=\n   proc(n)\n      if n = 1 then InitialValue else fcn(pric
e(n-1))\n      fi\n   end:\n\nfor n from 1 to 20 \n    do printf(`%4d \+
%10.4f`, n, price(n));\n    print();\n    od;\n\nplot([seq([n, price(n
)], n = 1 .. 20)], \n        year = 1 .. 20, title = `Prices`);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 88 "Yo
u can answer the questions about discrete dynamical systems by changin
g the value of  " }{TEXT 257 12 "InitialValue" }{TEXT -1 7 "  and  " }
{TEXT 258 1 "k" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 135 "The cell below shows how Maple can be us
ed to estimate the solution of initial value problems like the example
 in the browser window.  " }{TEXT 259 15 "Evaluate it now" }{TEXT -1 
1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 223 "with(plots):\n\nk := 0.0002:\nInitialValue := 0.50:
\n\ndiffeq := diff(p(t), t) = k*(Demand(p(t)) - Supply(p(t))):\n\nIVP \+
:= \{diffeq, p(0) = InitialValue\}:\n\nsolution := dsolve(IVP, \{p(t)
\}, numeric):\n\nodeplot(solution, p(t), 0..20);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 119 "You can answer th
e questions about initial value problems, or continuous dynamical syst
ems, by changing the values of  " }{TEXT 260 12 "InitialValue" }{TEXT 
-1 5 " and " }{TEXT 261 1 "k" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}}{MARK "1 0 0" 13 }{VIEWOPTS 1 1 0 1 1 1803 }