function fsm = fourier_movie(f,x,a,b,c,d,n)

% This animates the first n partial sums of the Fourier series of the 
% expression f on the interval [a,b].  The function is assumed to be 
% periodic with period L = b-a. The vertical axis goes from c to d. 
L = (b-a);
X = a:0.001:b;
g = inline(vectorize(f));

partsum = 1/L * double(int(f,x,a,b));
for k =1:n 
    partsum = partsum ...
        + 2/L*double(int(f*sin(2*k*pi*x/L),x,a,b))*sin(2*k*pi*x/L) ... 
        + 2/L*double(int(f*cos(2*k*pi*x/L),x,a,b))*cos(2*k*pi*x/L);
    ps2 = inline(vectorize(partsum));
    plot(X,g(X),'r'), hold on
    plot(X,ps2(X)), hold off
    axis([a b c d])
    fsm(k) = getframe;
end