Exercises

Please complete each exercise or answer the question before reviewing the posted solution comments.

Use the clear command before starting your work on a new problem to ensure that any existing variable name assignments don't interfere with your work on the new problem.

1. Plot the function over the domain -2 to 4.

        x = -2 : 0.2 : 4 ;
        y = 3.5 .^(-0.5.*x) .* cos(6*x) ;
        plot( x, y )

   Notice that element-wise operators must be used for the power and multiplication operations. But, why didn't we have to use the element-wise multiplication operator for the 6*x operation? Review the notes on Operators if you don't know.

   

2. Plot the polynomial f(x) = 4x3 + -5x2 + 3x - 7 over the domain x=-2..3.

       x = -2 : 0.1 : 3
       plot ( x, 4.*x.^3-5.*x.^2+3.*x-7 )

   Notice that you can enter the function inside the plot command. Though, we recommend that you define a function for a complex polynomials like this. The next lesson shows you how.

   

3. Plot the finite Fourier series given by the sum: on the interval x=(0,8π). The plot you should see is called the 'sawtooth function'.

   Here's an algorithm (set of steps) for solving this problem without iteration (loops):

   1. Create a vector for all n values in the sum.
   2. Create a different vector for a bunch of x values in the range.
   3. Use the sum command.
   4. Create the y vector
   5. Plot the results.
   

   Note: There will be other ways to solve this problem when you learn about iteration in programming.

        clear;
        figure;
        n = 1:1000 ;
        x = (0:0.1:8)*pi;
   	
        SinNX = sin(n'*x);
        SinNXOverN = diag(1./n) * SinNX;
   	
        SawTooth = sum( SinNXOverN );
   	
        plot( x, SawTooth );
        axis([x(1) x(length(x)) -pi/2 pi/2])
        title('Saw Tooth')