  We calculate the gravitational corrections to the effective action of N=2
SU(2) Seiberg-Witten theory with matter using modularity, the holomorphic
anomaly equation and expected behavior at the boundaries of the moduli space.
As in pure gauge theory we show that the gap condition at the dyon
singularities completely fixes the gravitational corrections. We discuss the
behavior of the gravitational corrections at the conformal points. We compare
our results with the recursive solution of the loop equation in the matrix
model approach, which provides in addition open amplitudes.
