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

Holomorphicity and Modularity in Seiberg-Witten Theories with Matter