%
%   EIGENF1.M   Demo of Fourier Series Representation for f(x) = 1
%
%   The goal here is to evaluate the infinite series expansion for 
%   f(x) = 1 in terms of sinusoids (i.e. a Fourier series expansion)
%
%   For normalized eigenfunctions, the coefficients and basis functions
%   are:
%      an = 2*sqrt(2/pi)/m   gn(x) = sqrt(2/pi)*sin(mx)  
%   with m = (2n-1)   and n = 1, 2, ...
%
%   For unnormalized eigenfunctions, the coefficients and basis functions
%   are :
%      an = (4/pi)/m         gn(x) = sin(mx)          
%   with m = (2n-1)   and n = 1, 2, ...
%
%   File prepared by J. R. White, UMass-Lowell (original Nov. 1996)
%     --> minor modifications (Aug. 1998)
%

%
%   getting started
      clear all, close all
%
%   set x domain
      x = linspace(0,pi,201);
      c = 4/pi;
%
%   calc 1st partial sum 
      s1 = c*sin(x);
%
%   calc 5th partial sum 
      s5 = s1;
      for n = 2:5
        m = 2*n-1;   s5 = s5 + (c/m)*sin(m*x);
      end
%
%   calc 20th partial sum 
      s20 = s5;
      for n = 6:20
        m = 2*n-1;   s20 = s20 + (c/m)*sin(m*x);
      end
%
%   calc 50th partial sum 
      s50 = s20;
      for n = 21:50
        m = 2*n-1;   s50 = s50 + (c/m)*sin(m*x);
      end
%
%   plot curves
      v = [0 pi 0 1.4];
      subplot(2,1,1),plot(x,s1,'g-',x,s5,'r--'),grid,axis(v)
      title('Truncated Fourier Series Approx to f(x) = 1')
      ylabel('Approx f(x) = 1')
      legend('1st PSum','5th PSum')
%
      subplot(2,1,2),plot(x,s20,'g-',x,s50,'r--'),grid,axis(v)
      xlabel('x-values'),ylabel('Approx f(x) = 1')
      legend('20th PSum','50th PSum')
%
%   end of demo
%