Green's functions with applications

by Duffy, Dean G.

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Title Statements

Full title :Green's functions with applications / Dean G. Duffy, Former Instructor, US Naval Academy, Annapolis, Maryland, USA.

Summary

Since publication of the first edition over a decade ago, Green's Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green's function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect the current state of the art. The book opens with necessary background information: a new chapter on the historical development of the Green's function, coverage of the Fourier and Laplace transforms, a discussion of the classical special functions of Bessel functions and Legendre polynomials, and a review of the Dirac delta function. The text then presents Green's functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. Detailing step-by-step methods for finding and computing Green's functions, each chapter contains a special section devoted to topics where Green's functions particularly are useful. For example, in the case of the wave equation, Green's functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Green's functions, worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas are featured throughout the text. A new chapter on numerical methods closes the book. Included solutions and hundreds of references to the literature on the construction and use of Green's functions make Green's Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering. Features: --Provides a systematic approach to the various methods available for deriving a Green's function. --Reviews the historical development of the Green's function, the Fourier and Laplace transforms, the classical special functions of Bessel functions and Legendre polynomials, and the Dirac delta function. --Presents Green's functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. --Includes worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas. --Contains a new numerical methods chapter as well as hundreds of references to the literature on the construction and use of Green's functions. Dean G. Duffy is with the National Aeronautics and Space Administration's Goddard Space Flight Center, Greenbelt, Maryland, USA. Publisher's note.

Edition Statements

Publication Date:2015
Edition:Second edition

Publication Statements

Publisher(s):CRC Press, Taylor & Francis Group
Place of Publication:Boca Raton
Language:eng
Publication Date:2015

The Physical Object

Description:xvii, 667 pages : : illustrations ; : 25 cm.

Edition Identifiers

ISBN:9781482251029, 1482251027, 9781138894464, 113889446X
oclc:ocn929866367
LC Classification:QA371
Dewey Decimal:515/.35

Chapter 1. Historical development -- chapter 2. Background material -- chapter 3. Green's functions for ordinary differential equations -- chapter 4. Green's functions for the wave equation -- chapter 5. Green's functions for the heat equation -- chapter 6. Green's functions for the Helmholtz equation -- chapter 7. Numerical methods.