Green's Functions and Linear Differential Equations: Theory, Applications, and Computation

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Prem K. Kythe

Green's Functions and Linear Differential Equations

Theory, Applications, and Computation

Prem K. Kythe

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English

Chapman & Hall/CRC
14 October 2024

Differential calculus & equations; Applied mathematics; Mathematical physics; Technology, Engineering & Agriculture

Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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.

By: Prem K. Kythe
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 703g
ISBN: 9781032920825
ISBN 10: 1032920823
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science
Pages: 382
Publication Date: 14 October 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Prem K. Kythe is a professor emeritus of mathematics at the University of New Orleans. Dr. Kythe is the co-author of Handbook of Computational Methods for Integration (CRC Press, December 2004) and Partial Differential Equations and Boundary Value Problems with Mathematica, Second Edition (CRC Press, November 2002). His research encompasses complex function theory, boundary value problems, wave structure, and integral transforms.