function [A,h] = mesheig(n)
%
%  Returns the matrix in the eigenvalue problem to solve
%  solve y" + w^2*y = 0, using n nodes over [0,1],
%  with boundary value conditions y(0) = 0, y(1) = 0.
%
%  On entry :
%    n         number of internal nodes in [0,1].
%
%  On return :
%    A         tridiagonal matrix of the linear system,
%              defined by a mesh of finite differences;
%    h         space between the nodes x(k) = x(0) + k*h.
%
%  Example: 
%    [A,h] = mesheig(4);
%    [v,lambda] = eig(A);   % solve the eigenvalue problem
%    m = max(v(:,1));       % to scale 1st eigenvector
%    x = 0:h:1              % prepare plot: range for x
%    y = [0; v(:,1)/m; 0]   % first eigenvector
%    plot(x,y)
%
h = 1/(n+1);
A = zeros(n,n);
for k = 1:n-1
  A(k+1,k) = -1;
  A(k,k+1) = -1;
end;
for k = 1:n
  A(k,k) = 2;
end;