Green's Functions and Linear Differential Equations: Theory,
Applications, and Computation presents a variety of methods to
solve linear ordinary differential equations (ODEs) and partial
differential equations (PDEs). The 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 also contains a large number of examples and
exercises from diverse areas of mathematics, applied science, and
engineering. Taking a direct approach, the book first unravels the
mystery of the Dirac delta function and then explains its
relationship to Green's functions. The remainder of the text
explores the development of Green's functions and their use in
solving linear ODEs and PDEs. The author discusses how to apply
various approaches to solve initial and boundary value problems,
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. He also covers applications of Green's functions, including
spherical and surface harmonics. Filled with worked examples and
exercises, this robust, self-contained text fully explains the
differential equation problems, includes graphical representations
where necessary, and provides relevant background material. It is
mathematically rigorous yet accessible enough for readers to grasp
the beauty and power of the subject.
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