This is a phase I multicenter study designed to determine the maximal tolerated dose (MTD) and toxicity of dasatinib in combination with paclitaxel and carboplatin during the first cycle of treatment in patients with advanced or recurrent ovarian, peritoneal, and tubal carcinoma. The MTD will be defined as the highest dose at which no more than 1 of 6 evaluable patient experiences a dose-limiting toxicity (DLT) due to the combination of dasatinib, paclitaxel,and carboplatin during the first cycle of treatment.