MATLAB.7
                                                                  
Plotting Fourier Series
We plot the partial sums for the Fourier series for abs(x) on [-3,3].

First we compute the coefficients by hand.

a(0)=3 ,
a(m)=-6*(1-(-1)^m)/(m*pi)^2    for m>= 1 ,
b(m)=0 .                                                         
                                                                               
                                  
Next we make an M-file for the nth partial sum.

***********************************************************************
                                                         
function w=summ(x,n)

w=3/2;
for m=1:n
  w=w-cos(m*pi*x/3)*6*(1-(-1)^m)/(m*pi)^2;
end
                                                         
***********************************************************************

We want to compare summ(x,n) with the 6-periodic extension of abs(x) ( See the 
example in Lab Assignment.3 ) . Its M-file is 

*************************************************************
function w=f(x)
z=6*floor((x+3)/6);
y=x-z;
w=abs(y);
*************************************************************

Now we go to the command window and plot summ(x,12) and f(x) on [-6,7] .
 We use "hold on" and "hold off" to plot the graphs together.
 
************************************************************************

hold on
fplot('summ(x,12)',[-6,7])
fplot('f(x)',[-6,7]) 
hold off;                                                
                                                         
************************************************************************

To see how far apart the graphs are  find the maximum of abs(f(x)-summ(x,12)) .
( See Lab Assignment.2 ).

ASSIGNMENT 7  :

Let f(x)=x^2 for -2<=x<2 .

Find the Fourier series for f on [-2,2]. Plot the partial series for 
f,summ(x,8)
together with a plot of the 4-periodic extension of f(x) on [-5,6].

For what n is the maximum of abs(f(x)-summ(x,n)) on  [-5,6] less than 0.1?