Page 99
% make an m-file, delayFcn0.m:
%   function y=delayFcn0(t)
%   y = exp(t/10);
N=10; % # steps per unit interval
delT=1/N; % so delta t=0.1
% t is now linked to index i by t=-1+(i-1)*delT
% set init. val's via delay fcn f0
for i=1:N+1
   t=-1+(i-1)*delT; f(i)=delayFcn0(t);
end
% work from t=0 in steps of delT
% ending time tfinal = 2, ending index is n
% solve tfinal=-1+(n-1)*delT for n
n=(2+1)*N+1;
for i=N+1:n-1
   t=-1+(i-1)*delT;
   delY=f(i-N)*delT; %N back=delay of 1
   f(i+1)=f(i)+delY; % Eulers method
end
t=-1:delT:2; plot(t,f);

                      Page 101
% leastsquare for r in y=A*exp(rt)
A=2;
t=[1 2 3]; % time data 
y=[3 5 9]; % corresponding y data
lny=log(y)-log(A); % map to log and subtract bias
M=t';      % set up indep. variables M matrix
r=M\(lny') % and solve

                      Page 102
tt=[1790:10:1990];
pop=[3.929214 5.308483 7.239881 9.638453...
 12.866020 17.069453 23.191876 31.433321...
 39.818449 50.155783 62.947714 75.994575...
 91.972266 105.710620 122.775046...
 131.669275 151.325798 179.323175...
 203.302031 226.545805 248.709873];
plot(tt,pop,'o');

stt=0:10:200; % translated time

                     Page 103
lnPop=log(pop); plot(stt,lnPop,'o')

                     Page 104
MT=[stt; ones(1,21)];
params=MT'\(lnPop')
lnFit=params(2)+params(1)*stt
plot(stt,exp(lnFit))
hold on
plot(stt,pop,'o')

                   Exercises/Experiments

2.
yrs=[9,19,29,39,49,59,69,79,89];
DR=[.3,1.5, 1.9, 2.9, 6.5, 16.5,37, 83.5, 181.9];
plot(yrs,DR);% so data exp. like
lnDR= log(DR);
MT=[yrs;ones(size(yrs))];
% matrix of independent variable data
params=MT'\lnDR';
a=params(1); b=params(2);
fit=exp(b)*exp(a*yrs);
plot(yrs,DR,yrs,fit);