%% Animation of the partial sums of a Fourier Series

%%
% The command *fourier_movie* will let you animate the graphs of the
% partial sums $s_k,\  k=1,\dots,n$ of the Fourier series of the expression f on
% the interval [a,b].  f is assumed to be periodic with period L = b-a.
% (Notice, the period is L, not 2L). The command requires you to specify
% the limits on the vertical axis as well, since it creates the movie by
% making a frame at a time and you want the same axes for every frame. 
% You will want to download fourier_movie.m to use it.

type fourier_movie

%%
% We use this with f = abs(x) on [-1,1] and take the first 20 partial sums.
% First we create the frames.
syms x
f = abs(x)
absx=fourier_movie(f,x,-1,1,0,1,20)
%%
% We can view this with *mplay*.
mplay(absx)
%% 
% (I removed the output of the *mplay* commands from the html file because
% otherwide they 

%%
% We use it with f = x on [-1,1].  Since the convergence of the series is
% slower for this function, we take the first 50 partial sums.

f = x
xmovie=fourier_movie(f,x,-1,1,-1.2, 1.2,50)
%%
% You can also save it as *name.mat*  (replace "name" by the name you want)
% with the command *save('name','mymovie')* where mymovie is the name you
% gave the output of your fourier_movie command. The movie will then be
% named 'mymovie'. You can use different names for the two arguments in the
% save command, but when you load name.mat with the command *load('name')*, 
% the movie will be named mymovie. So, for example, if I have created the
% movie ahead of time with the command:

save('xmovie','xmovie')

%%
% I can view it with the commands:
load('xmovie')
mplay(xmovie)
%%
% We use it with the function f = exp(x) on [0,5].  I'll take 20 partial
% sums.

f = exp(x)

expmovie=fourier_movie(f,x,0,5,-20,200,20)
%%
mplay(expmovie)