Green Functions: Methods and Applications

This lecture covers methods to compute Green functions, including the image charge method and expansion in eigenfunctions of the Laplacian. It also discusses local Ohm's law, Joule heating, and surface pressure on conductors in the context of classical electrodynamics. The instructor explains how to determine the Green function for a given system, presents examples using the image charge method, and explores the expansion in eigenfunctions. The lecture delves into the unique solutions provided by these methods and their applications in electrostatics and magnetostatics. Additionally, it examines the simplest model of conductors based on Ohm's law and the behavior of conductors in electrostatics.