  We study the de Rham complex on a smooth manifold with a periodic end modeled
on an infinite cyclic cover X' \to X. The completion of this complex in
exponentially weighted L^2-norms is Fredholm for all but finitely many
exceptional weights determined by the eigenvalues of the covering translation
map H_*(X') \to H_*(X'). We calculate the index of this weighted de Rham
complex for all weights away from the exceptional ones.
