Green's Functions and Linear Differential Equations

Theory, Applications, and Computation
1. Auflage 2011
ISBN: 978-1-4398-4008-5
Verlag: CRC Press

Buch, Englisch, 382 Seiten, Format (B × H): 159 mm x 237 mm, Gewicht: 680 g

Reihe: 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.

Zielgruppe

Academic

Autoren/Hrsg.

Kythe, Prem K

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

Some Basic Results. The Concept of Green’s Functions. Sturm–Liouville Systems. Bernoulli’s Separation Method. Integral Transforms. Parabolic Equations. Hyperbolic Equations. Elliptic Equations. Spherical Harmonics. Conformal Mapping Method. Appendices. Bibliography. Index.

Über Autor(innen)

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.