Canonical Transforms: Hamilton-Jacobi Equation

This lecture covers the concept of canonical transforms and the Hamilton-Jacobi equation, focusing on the explicit solution of the system and the importance of initial conditions. It delves into the theory of differential equations, emphasizing the need for motion constants and the uniqueness of solutions. The instructor explains the process of finding explicit forms and the implications of the canonical equations, highlighting the significance of partial derivatives in re-solving the Hamilton-Jacobi equation.