  We present the Bogoliubov theory for the Bose-Einstein condensation of
Feshbach molecules in a balanced Fermi mixture. Because the Bogoliubov theory
includes (Gaussian) fluctuations, we can in this manner accurately incorporate
both the two-body and many-body aspects of the BEC-BCS crossover that occurs
near a Feshbach resonance. We apply the theory in particular to the very broad
Feshbach resonance in atomic Li-6 at a magnetic field of B_0 = 834 G and find
good agreement with experiments in that case. The BEC-BCS crossover for more
narrow Feshbach resonances is also discussed.
