This is NOT a required assignment for math 427K-H!!!!


This assignment is ment to be an introduction to matlab.  Matlab is installed
 on the Unix machines in RLM.  There is an undergraduate computer lab on the
 7th floor with unix machines.

What to turn in:  I want print outs of the code used to generate your answers
 followed by the output from matlab.  Make heavy use of copy/paste to do this.

1.Compute the following 3 difference equations.  
for the first 2 use the initial condition x_1 = 0.1
x_n = .7*x_(n-1)
x_n = 3.3*x_(n-1) * (1 - x_(n-1))  <-- note, this is nonline

for the last one use  x_1 = .2 and  x_2 = .5
x_n = .3*x_(n-1) - x_(n-2)  

I want you to print and label a graph of each difference equation.  Print the
 code used to generate one of these graphs.

I leave it up to you to determine how many iterations of each equation
 to compute, but I want the graphs to display the general behavior of the
 difference equations.  You may label the graphs by hand, but I'll give
 extra credit if you figure out how to have matlab label them for you.

The following code should help you get started
x1 = 0.1;
N = 20;
x(1) = x1;
for i = 2:N
    x(i) = 3.3*x(i-1);
    t(i) = i;
end
plot(t,x)

2.Create a 2X2, a 3X3, a 4X4, and a 5X5 matrix and compute the eigenvalues.
Hint: 
A = [[2, 3, 4]; [4, 6, 2]; [2, 7, 8]]
eig(A)

3.Open matlab help and do a search for the key word 'roots'  I want you
 to compute the roots of the polynomial
p(x) = -7x^3 + 4x^2 -.3x +1

(on back)
4.Find the solutions to the equation 3x^4 - .5x = 7x^2 + 1

5.  Use the fibonacci numbers to approximate the golden ratio.  There
 are several ways you can do this.  Basically I want convincing evidence
 that x_(n+1)/x_n approximates 1.618033...