Properties of Fundamental Solutions: Green's Representation Formula

This lecture covers the properties of fundamental solutions and introduces Green's representation formula. The theory of distributions is briefly introduced, followed by a detailed explanation of fundamental solutions of the Laplace equation. The lecture progresses to discuss various forms of fundamental solutions for the Laplace equation and their applications, including satisfying specific conditions. The instructor delves into the theory behind Green's representation formula and its significance in solving partial differential equations. The lecture concludes with a thorough analysis of fundamental solutions and their behavior in different scenarios.