One of the fundamental problems of field theory1 is the construction of solutions to linear differential equations when there is a specified source and the differential equation must satisfy certain boundary conditions. The purpose of this book is to show how Green’s functions provide a powerful method for obtaining these solutions. In this chapter, we present a historical overview of their evolution.
1.1 Mr. Green’s Essay
In 1828 George Green (1793–1841) published an Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnetism. In this seminal work of mathematical physics, Green ...