Lecture
This lecture covers the classification of Partial Differential Equations (PDEs) into linear, semi-linear, and quasi-linear types based on the linearity of the function F and its partial derivatives. It explains the definitions of these classifications and provides examples of each type of PDE. The lecture also delves into the properties of solutions to such PDEs, emphasizing the significance of the eigenvalues of the associated matrices. Additionally, it discusses the classification of second-order linear PDEs, focusing on elliptic, parabolic, and hyperbolic types. The lecture concludes with a detailed explanation of domains with smooth boundaries and the application of Gauss-Green formula and integration by parts in the context of PDEs.