This lecture covers the application of the divergence theorem to analyze flux through closed volumes, subdividing them into sub-volumes for convenience and asserting the equality of fluxes through their surfaces. The instructor explains the cancellation of internal fluxes and the simplification of calculations, leading to a clear understanding of the flux behavior. The lecture also delves into the concept of control volumes, uniaxial motion, and the evolution of material volumes over time, providing a comprehensive overview of flux analysis in closed systems.