Explain the conjugate beam method for calculating deflections.

The conjugate beam method calculates deflections by treating the M/EI diagram as a load on a conjugate beam with modified supports (fixed becomes free, pinned stays pinned, free becomes fixed). The shear in the conjugate beam equals the slope in the real beam, and the moment in the conjugate beam equals the deflection in the real beam. This method is particularly useful for beams with varying cross-sections or complex loading.