Green's Functions and Linear Differential Equations - Prem K. Kythe

Green's Functions and Linear Differential Equations

Theory, Applications, and Computation

(Autor)

Buch | Hardcover
382 Seiten
2011
Chapman & Hall/CRC (Verlag)
978-1-4398-4008-5 (ISBN)
168,35 inkl. MwSt
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.

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.

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.

Erscheint lt. Verlag 8.3.2011
Reihe/Serie Chapman & Hall/CRC Applied Mathematics & Nonlinear Science
Zusatzinfo 9 Tables, black and white; 47 Illustrations, black and white
Sprache englisch
Maße 156 x 234 mm
Gewicht 657 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Technik Umwelttechnik / Biotechnologie
ISBN-10 1-4398-4008-3 / 1439840083
ISBN-13 978-1-4398-4008-5 / 9781439840085
Zustand Neuware
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