This lecture covers the implementation of initial and boundary conditions for waves in inhomogeneous media, including the explicit 3-level diagram, numerical stability, and the propagation of waves in one-dimensional mediums. The lecture also discusses the superposition principle, eigen modes, and eigen frequencies, as well as the application of boundary conditions for wave propagation. Various edge conditions and the use of finite differences for derivatives are explored, along with examples of shallow water waves. The lecture concludes with exercises on wave exit conditions and the impact of different equations on wave propagation.