% script to plot Fourier series representation of 
% the derivative of the triangle function
% M is number of Fourier terms
% N is number of x values in [0,1]
% M and N must be supplied from outside

m=1:M;  %m labels the Fourier terms
x=linspace(0,1,N); %x is the independent variable
FourierCoef=4*sin(m*pi/2)./m/pi;  %Fourier coefficients for diff(triangle)
CosFunctions=cos(pi*m'*x);  %the jth row of this matrix is cos(j*pi*x)
plot(x,FourierCoef*CosFunctions)  %plot the function defined by the Fourier series

%line 10 above uses a non-obvious trick to construct an MxN matrix as m'*x,
%then take the cosine of it, meaning the sine of each element.

%A more straightforward set of commands to do this would be
%CosFunctions=[];   (empty matrix)
%for j=1:M  (beginning of a loop, a different j for each pass through)
%CosFunctions=[CosFunctions; cos(pi*j*x)];  (append the jth row)
%end  (end the loop)
% .. This loop constructs the matrix row by row