%% CREATING A MOVIE OF CONVERGENCE OF A FOURIER SERIES %% Creating a movie % The command *fourier_movie* will create an animation or movie of the first n % partial sums of the Fourier series of the expression f on the interval % [a,b]. You will want to download fourier_movie.m to use it. % Here is the code for the command. type fourier_movie %% Example 1: ||x|| syms x f = abs(x); a= -1; b=1; n=20; %% % This command creates the movie. absx = fourier_movie(f,x,-1,1,20); %% Viewing the movie % You can view it with *mplay*. mplay(absx) %% Saving the example % You can 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. Then you can load it % during another MATLAB session with the command *load('name')*. The movie will % then be named 'mymovie'. This command saves the example as absx.mat. save('absx','absx') %% % 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. % % You can close mplay windows with the command close all hidden %% Example 2: x % 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,-1,1,50); %% mplay(xmovie) close all hidden %% Example 3: exp(x) % I'll take 20 partial % sums on [0,5]. f = exp(x) expmovie = fourier_movie(f,x,0,5,20); %% mplay(expmovie)