%
% evec.m
%
% compute and display the first K eigenvectors of the
% the N-by-N second difference matrix for a cell of length ell
%

function evec(ell,N,K)

dx = ell/N;	
x = dx/2:dx:ell-dx/2;

S = (2*eye(N)-diag(ones(N-1,1),1)-diag(ones(N-1,1),-1))/dx/dx;
S(1,1) = 1/dx/dx;
S(N,N) = 1/dx/dx;

[Q,Z] = eig(S);

z = diag(Z);

z(1:K)

stairs(x,Q(:,1:K))
a = axis;
xlabel('x  (cm)','fontsize',16)
ylabel('eigenvector','fontsize',16)
axis([0 pi a(3) a(4)])