Section 6.2

Maple Tool 2

This Maple file is designed to be used with Activity 3 in Section 6.2.

>	with(plots):with(DEtools):

Warning, the name changecoords has been redefined

We begin by displaying the slope field for the differential equation

with the values of  and  given below.

>	K:=0.00009; M:=1000;

>	Slope:=DEplot(diff(P(t),t)=K*P(t)*(M-P(t)),P(t), t=0..100,P=0..1200,stepsize=1, thickness=2, linecolor=black):%;

Next we set up the Euler's Method approximation and plot this om the slope field. Enter your value of  in this calculation. (Note that this is the same calculation as was used in Maple Tool 1 in this section.)

>	n:=40; Delta:=120/n; t:=k->k*Delta; P := proc(k)

>	P(k) := P(k-1)+K*P(k-1)*(M-P(k-1))*Delta;

>

end:

>	P(0):=111; solution:=[seq([t(k),P(k)],k=0..n)]: Euler:=plot(solution, t=0..120, P=0..1000, style=point,symbol=circle, color=blue, thickness=2, xtickmarks=[20,40,60,80,100], ytickmarks=[200,400,600,800,1000]):

>	display(Euler,Slope);

>

>