  We show that the study of the collective oscillations in a harmonic trap
provides a very sensitive test of the equation of state of a Fermi gas near a
Feshbach resonance. Using a scaling approach, whose high accuracy is proven by
comparison with exact hydrodynamic solutions, the frequencies of the lowest
compressional modes are calculated at T=0 in terms of a dimensionless parameter
characterizing the equation of state. The predictions for the collective
frequencies, obtained from the equations of state of mean field BCS theory and
of recent Monte-Carlo calculations, are discussed in detail.
