Partial Differential Equations: Characteristics and Solutions

This lecture covers the concept of characteristic curves in partial differential equations, focusing on the existence and uniqueness of solutions. The instructor explains the normal derivative, non-characteristic valleys, and offset in the context of semi-linear cases. The lecture also delves into the change of variables, homomorphisms, and the Cauchy problem. Emphasis is placed on determining solutions with Cauchy conditions and understanding the behavior of functions in different domains. The presentation concludes with discussions on non-intervention scenarios and discontinuity lines, providing a comprehensive overview of solving EDPs.