Page 154 with(LinearAlgebra): el:=Matrix(7,7); # Maple initializes the entries to 0 # symbolic maple calculations require rational numbers, e.g. # .08 = 2/25, .28 = 7/25 and so on el[1,5]:=2/25: el[1,6]:=7/25: el[1,7]:=21/50: el[2,1]:=657/1000: el[3,2]:=93/100: el[4,3]:=93/100: el[5,4]:=93/100: el[6,5]:=935/1000: el[7,6]:=935/1000: el; evalm(el &* [P0,P1,P2,P3,P4,P5,P6]); Page 155 el10:=evalf(evalm(el^10)): Digits:=2; evalf(evalm(el10)); Digits:=10; vel:=evalf(Eigenvects(el)); vals:=vel[1]; lambda:=vals[1] # only one real e-value, should be the first # grab the first e-vector and normalize it vects:=(Transpose(vel[2]): pf:=vects[1]; pf:=[seq(V[i]/V[1],i=1..7)]: pf:=convert(pf,Vector[column]); Page 156 chk:=[1,el[2,1]/lambda, el[2,1]*el[3,2]/lambda^2, el[2,1]*el[3,2]*el[4,3]/lambda^3, el[2,1]*el[3,2]*el[4,3]*el[5,4]/lambda^4, el[2,1]*el[3,2]*el[4,3]*el[5,4]*el[6,5]/lambda^5, el[2,1]*el[3,2]*el[4,3]*el[5,4]*el[6,5]*el[7,6]/lambda^6]; evalf(evalm(el10 &* [1,1,1,1,1,1,1])); evalm(lambda^10*V); Page 159 P:=(n,t)-> h(n-t)*exp(-int(mu(n-t+u,u),u=0..t)); diff(P(n,t),t)+diff(P(n,t),n)+mu(n,t)*P(n,t); simplify(%); Exercises/Experiments 1. restart; for n from 0 to 100 do P[n,0]:=(100-n)*(25+n); mu[n]:=.0524*(exp(.03*n)-1); od: plot([seq([i,P[i,0]],i=0..100)]); plot([seq([i,mu[i]],i=0..100)]); for t from 1 to 3 do P[0,t]:=(1.9/20)* sum(P[i,t-1],i=21..30); for k from 1 to 100 do P[k,t]:=(1-mu[k-1])*P[k-1,t-1]; od: od: for t from 0 to 3 do total[t]:=sum(P[i,t],i=0..100); od;