What methods are used to calculate beam deflections?

Common methods include: Double integration (solving EI d²y/dx² = M), Macaulay's method (for multiple loads using singularity functions), Moment-area theorems (graphical approach), Conjugate beam method (treating M/EI as load), and Energy methods (Castigliano's theorem). Each has advantages: double integration is fundamental, Macaulay handles complex loading, and energy methods suit indeterminate structures.