% Eigenvalue problem u'' = \lambda u

clear all; close all
a=0; b=pi; n=100; N=n-1;
h=(b-a)/n;
x=h:h:b-h;

% form the matrix
A = diag(2*ones(1,N))+ diag(ones(1,N-1),1) + diag(ones(1,N-1),-1);
A = A/(h*h);
d = eig(A);  figure(1); plot(d)
[V,D]=eig(A);n1=fix(n/4);n2=fix(n/2);
u1=V(:,1); u2=V(:,n1);u3=V(:,n2);u4=V(:,n-2);
figure(2)
subplot(221); plot(x,u1)
subplot(222); plot(x,u2)
subplot(223); plot(x,u3)
subplot(224); plot(x,u4)

% Note: the eigen-functions are normalized in 2-norm.