Wave Equation Separation of Variables

This lecture covers the method of separation of variables for the wave equation on [0, L], focusing on the consequences of boundary conditions, solving two sub-problems for V and W separately, and combining solutions to form a general solution. The instructor explains the Sturm-Liouville problem, solutions for V and W, and the importance of Fourier coefficients in satisfying initial and boundary conditions. The lecture concludes with the superposition step and the consideration of initial conditions, leading to the complete solution of the wave equation with detailed mathematical derivations and explanations.