  A sum rule approach is used to calculate the zero temperature oscillation
frequencies of a two component trapped atomic Fermi gas in the BCS-Bose
Einstein condensation crossover region. These sum rules are evaluated using a
local density approximation which explicitly includes Feshbach molecules.
Breathing modes show non-monotonic behavior as a function of the interaction
strength, while quadrupole modes are insensitive to interactions for both
spherically symmetric and axially symmetric traps. Quantitative agreement is
found with experiments on atomic $^6Li$ system and with other theoretical
approaches.
