Math 414-700 - Spring 2004

Assignment 1

• Read sections 1.1-1.2.
• Problems
  1. Matlab assignment. Download the linked m-file part_sum_c.m . This can be used to plot trigonometric polynomials of the form

     y(t) = a₀ + a₁cos(t)+ b₁sin(t) + a₂cos(2t)+ b₂sin(2t) + ... + a_ncos(nt)+ b_nsin(nt)

     In the m-file (program), the arguments are as follows:

     a=[a₀, a₁ ,..., a_n]

     b=[b₁, b₂ ,..., b_n]

     t=row containing times at which y(t) is evaluated.

     A=½ period. (Ignore this for now.)

     Here is an example of how this is used. Suppose we want to plot y=1+2cos(t)+3sin(t)-sin(3t) on [0,4π]. To do this, we type the lines below, hitting return after each line.

     a = [1,2,0,0];

     b = [3,0,-1];

     t = linspace(0,4*pi,500);

     y = part_sum_c(a,b,t);

     plot(t,y)

     xlabel('t'), ylabel('y'), title('y=1+2cos(t)+3sin(t)-sin(3t)')

     Be careful about the backquote ' . This needs to be in the code; it indicates the start and finish of a character string. Check the Matlab documentation for exporting the figure. Include the plot in your homework. Do the same for these trigonometric polynomials:
     1. y=3cos(t)-2sin(t)+½cos(2t)+½sin(2t)
     2. y=sin(t)+sin(2t)/2+sin(3t)/3+sin(4t)/4 (Note: just set a=0).
     3. y=cos(t)+cos(3t)/3²+cos(5t)/5² (Note: just set b=0).

  2. §1.4: 1, 7, 21

• Due Wednesday, 1/28/03