Math 340 Exam 1, Oct. 28, 2013
Name:_
Problem 1 (25 points)
Write a program that, for input
iteration
generates sequences cfw_
Execute your program using
and
by the
Then plot the set of points
Problem 2 (10 points)
Rewrite the following sum into a Sigma/P
Math 340 Exam 1 Answer
Problem 1 (25 points)
Write a program that, for input x0, y0, n, generates sequences cfw_ x0, x1, ., xn and
iteration
2
2
xk C 1 = xk K yk C 0.9$xk K 0.6013$yk
yk C 1 = 2$xk$yk C 2$xk C 0.27$yk
Then plot the set of points xj, yj
j =
Math 340 Exam 1, Oct. 24, 2011
1. Write a program to carry out the iteration for calculating
generate 50 correct digits of :
. Use your program to
2. Write the following sum in Sigma notation, and write a program to calculate the first n
terms of the sum:
Problem 1.
Borwein := proc(n)
local a, s, r, k;
a[0] := 1/3;
s[0] := (sqrt(3)-1)/2;
for k from 0
r[k+1] :=
s[k+1] :=
a[k+1] :=
end do;
to n-1 do
3/(1+2*(1-s[k]^3)^(1/3);
(r[k+1]-1)/2;
r[k+1]^2*a[k]-3^k*(r[k+1]^2-1);
return evalf(1/a[n]);
end proc;
read("e
Math 340 Exam 1
Oct. 23, 2012
1. (25 points) A discrete dynamic system, the Gingerbreadman map, is given as an iteration: Starting from a point
(x0,y0), iterate according to the formula
xk+1 = 1-yk +|xk |, yk+1 = xk k = 0, 1, 2,
Write a program that, for