  We describe a strategy for computing Yukawa couplings and the mirror map,
based on the Picard-Fuchs equation. (Our strategy is a variant of the method
used by Candelas, de la Ossa, Green, and Parkes in the case of quintic
hypersurfaces.) We then explain a technique of Griffiths which can be used to
compute the Picard-Fuchs equations of hypersurfaces. Finally, we carry out the
computation for four specific examples (including quintic hypersurfaces,
previously done by Candelas et al.). This yields predictions for the number of
rational curves of various degrees on certain hypersurfaces in weighted
projective spaces. Some of these predictions have been confirmed by classical
techniques in algebraic geometry.
