We present the Bogoliubov theory for the Bose-Einstein condensation of Feshbach molecules in a\ud balanced Fermi mixture. Because the Bogoliubov theory includes (Gaussian) fluctuations, we can\ud in this manner accurately incorporate both the two-body and many-body aspects of the BEC-BCS\ud crossover that occurs near a Feshbach resonance. We apply the theory in particular to the very\ud broad Feshbach resonance in atomic 6Li at a magnetic field of B0 = 834 G and find good agreement\ud with experiments in that case. The BEC-BCS crossover for more narrow Feshbach resonances is\ud also discussed
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