GreenÆs Functions and Linear Differential Equations: Theory, Applications, and Computation

This self-contained book unravels the mystery of the Dirac delta function and explains its relation to Green's functions. It presents Green's functions for linear ODEs and PDEs and uses the methods of Bernouilli's separation, integral transforms, and conformal mapping to solve boundary value problems and various applications, including spherical and surface harmonics. The text also describes an interpolation method to numerically construct Green's functions for convex and star-like regions. It includes numerous examples and exercises from diverse areas of mathematics, physics, and engineering.