% programita para la serie de senos y cosenos de f(x) = x
% -L \le x \le L

L = 1;
margen = 0.1;

a0 = 2*L;


for N = [1 3 5 15 25]

  n=[1:N];
  a = zeros(size(n));
  b = -(2*L) ./ (n*pi);

  x = [0:0.01:2*L];
  npix = pi*(n'*x);
  fap = a0/2 + a * cos(npix) + b * sin(npix);

  f = x;

  M = max([f fap]);
  m = min([f fap]);
  plot(x,f,'r',x,fap,'m',[-2*L 2*L],[0 0],'b',[0 0],[-M M],'b');
  title(sprintf('N = %d',N))
  axis([0-margen 2*L+margen m-margen M+margen])
  pause
end
pause

ff = f;

for N = [1 3 5 15 25]

  n=[1:N];
  a = zeros(size(n));
  b = -(2*L) ./ (n*pi);

  x = [-2*L:0.01:4*L];
  npix = pi*(n'*x);
  fap = a0/2 + a * cos(npix) + b * sin(npix);

  f = x;

  M = max([f fap]);
  m = min([f fap]);
  plot(x,f,'r',x,fap,'m',[-2*L 4*L],[0 0],'b',[0 0],[m M],'b');
  axis([-2*L-margen 4*L+margen m-margen M+margen])
  title(sprintf('N = %d   error = %.8f',N,max(abs(f-fap))))
  pause
end
pause

ff(end) = [];
f = [ff ff ff 0];
plot(x,f,'r',x,fap,'m',[-2*L 4*L],[0 0],'b',[0 0],[m M],'b');

axis([-2*L-margen 4*L+margen m-margen M+margen])