Partial Differential Equations: First Order

This lecture covers the concept of quasi-linear first-order partial differential equations (PDEs) involving functions of two variables, discussing the d'Alembert formula and the verification of solutions. It also introduces the notion of characteristic curves and surfaces in the context of PDEs, emphasizing the importance of solutions' verification. The lecture delves into the definition and properties of characteristic curves, highlighting their role in determining unique solutions. Additionally, it explores the conditions for the existence of classical solutions and the terminology related to characteristic curves. The lecture concludes with a discussion on the uniqueness of solutions and the significance of characteristic curves in solving PDEs.