  In this work, we present a theoretical study for the collective oscillation
modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi
superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid
to a molecular Bose-Einstein condensate (BEC) in harmonic trapping potentials
with cylindrical symmetry of experimental interest. To this end, we start from
the coupled superfluid hydrodynamic equations for the dynamics of Bose-Fermi
superfluid mixtures and use the scaling theory that has been developed for a
coupled system. The collective oscillation modes of Bose-Fermi superfluid
mixtures are found to crucially depend on the overlap integrals of the spatial
derivations of density profiles of the Bose and Fermi superfluids at
equilibrium. We not only present the explicit expressions for the overlap
density integrals, as well as the frequencies of the collective modes provided
that the effective Bose-Fermi coupling is weak, but also test the valid regimes
of the analytical approximations by numerical calculations in realistic
experimental conditions. In the presence of a repulsive Bose-Fermi interaction,
we find that the frequencies of the three collective modes of the Bose and
Fermi superfluids are all upshifted, and the change speeds of the frequency
shifts in the BCS-BEC crossover can characterize the different groundstate
phases of the Bose-Fermi superfluid mixtures for different trap geometries.
