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% readmeFouSer
% Contents of this directory
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% 18.385 (Nonlinear Dynamical Systems). MIT, Fall 1999. R. R. Rosales.
%
% fourierSC ...... Illustrates the convergence of the Fourier Series of a 2*pi
% periodic function F(x) to the function as more & more terms
% are added. Several functions F(x) are provided in a menu of
% examples, with an option for the user to add his own.
% heatSln ........ Displays the solution of the heat equation T_t = T_xx as a
% function of time, with initial conditions given by the same
% functions F(x) used by fourierSC. Illustrates the use of
% spectral techniques for the numerical solution of PDE's.
% FSFun .......... User provided function for input into fourierSC or into
% heatSln, selected when OPTION=0 is picked. Must be in the
% directory from which the user is running MatLab. Given an
% array containing the x variable, it must produce the array
% y with the values of the function.
% Example of a FSFun.m file:
%
% function y = FSFun(x)
% %
% y = (x.^2).*(x-2*pi).^2;
%
% Note the use of vector operands here (.* and .^) required
% because both x and y are arrays. The array x is defined in
% both fourierSC and heatSln by: x = 0:dx:2*pi-dx --- some dx
% that depends on the (user prescribed) resolution.
% >>>>>>>> Check help FSFun for important details about how to define
% the function when dealing with discontinuities!
% >>>>>>>> NOTE: help FSFun will NOT work if the current directory for
% MatLab has a user constructed FSFun.m file already in it.
% FSoption ....... Script to construct the functions F(x) used by heatSln and
% fourierSC ("fancy", with buttons).
% FSoptionP ...... Same as FSoption, but without buttons.
% gibbsFSE ....... Illustrates the GIBBS phenomenon for convergence of Fourier
% series near discontinuities.
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help readmeFouSer
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