Green Functions: Theory and Applications

This lecture covers the theory and applications of Green functions in classical electrodynamics. Starting with an overview of Maxwell's equations in both integral and differential forms, the instructor explains the concept of gauge invariance and its implications. The lecture then delves into boundary conditions, uniqueness of solutions, and the role of Green functions in solving Poisson's equation. Various methods for finding the Green function are discussed, including the image charge method and expansion in eigenfunctions of the Laplacian. The importance of choosing the appropriate Green function based on boundary conditions is emphasized, along with practical examples and proofs.