Define the integrand using the given definition as

Question

1. Roots of Polynomial.

p(x) = x⁵ - 2x + 3

(a) Demonstrate how to store the above polynomial as p = . . . in Matlab.
(b) Find the roots of the stored polynomial and show as r = . . . .

2. Find the roots of the following function.

f(z) = z² + 2iz +3

3. Recall integration by the use of the path along C using the parametric representation.

Now we have a complex function f(z) = z²2z + 1 and the contour C expressed as x = y²+ 1; ( 2 < y < 2) .

(a) Find a parametric representation of C using Matlab ( Let y = t. ).

This means that you need to find z(t).
First define y using t and then x.
You can then use the command the simple to define z.

(b) Store the given function f(z) as f = . . . and define the integrand (left hand side of the integral symbol) using the given definition as Integrand = . . . .

(c) Calculate the integration along the given path using the int command as F = . . . . You need to convert the result to a numerical answer using the double command.

4. You can generate random numbers using Matlab command. Type,

randn('seed', 1);
x=randn(1000,1);
y=randn(1000,1);

Now calculate the following values.
(a) the mean of x;
(b) the median of x;
(c) the standard deviation of x;
(d) the interquartile range of x;
(e) the correlation matrix of x; y
(f) plot a histogram of x; with 50 intervals.