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GREEN’S FUNCTIONS WITH APPLICATIONS Second Edition

Chapter 1 Historical DevelopmentOne of the fundamental problems of field theory1is the constructionof solutions to linear differential equations when there is a specified sourceand the differential equation must satisfy certain boundary conditions. Thepurpose of this book is to show how Green s FUNCTIONS provide a powerfulmethod for obtaining these solutions. In this chapter, we present a historicaloverview of their MR. GREEN S ESSAYIn 1828 George Green(1793 1841) published anEssay on the Applicationof Mathematical Analysis to the Theory of Electricity and Magnetism.

solving (in the case of Sturm-Liouville problem) d dx % f(x) dg dx & +p(x)g = −δ(x−ξ)(1.1.7) with homogeneous boundary conditions, where δ(x − ξ) was the recently in-troduced delta function by Dirac. The advantage of this formulation was that the powerful techniques of eigenvalue expansions and transform methods

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