Green's Functions and Linear Differential Equations
Theory, Applications, and Computation
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This self-contained book unravels the mystery of the Dirac delta function and explains its relation to Greena (TM)s functions. It presents Greena (TM)s functions for linear ODEs and PDEs and uses the methods of Bernouillia (TM)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 Greena (TM)s functions for convex and star-like regions. It includes numerous examples and exercises from diverse areas of mathematics, physics, and engineering.
This self-contained text provides a sufficient theoretical basis to understand Green's function method, which is used to solve initial and boundary value problems involving linear ODEs and PDEs. It presents a variety of approaches, including classical and general variations of parameters, Wronskian method, Bernoulli's separation method, integral transform method, method of images, conformal mapping method, and interpolation method. The text also covers applications of Green's functions and contains numerous examples and exercises from diverse areas of mathematics, applied science, and engineering.
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