University of Florida/Egm4313/s12.team11.gooding/R6

R6.3

edit

Problem Statement

edit

Page 491, #15,17. Plot the truncated Fourier series for n=2,4,8.

Solution

edit

15.


 

Since  , the function is odd.

 
After simplification,  
. Using Equation (5) on page 490, the exapansion becomes;
 
With   this becomes;
  for n is "odd".
This means when n is even,  

 

17.
 

 

 
 

  

 
Simplifying results in;
 
So,

  

when n is odd.
 
Simplifying results in;

 

 

Since   for even n,   becomes   for even n.