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Green's Functions with Applications: Advances in Applied Mathematics

Autor Dean G. Duffy
en Limba Engleză Hardback – 16 mar 2027
Since its first publication, Green's Functions with Applications has been the definitive resource for applied scientists and engineers seeking systematic methods for deriving Green's functions across a wide range of differential equations. This thoroughly revised third edition updates the content to reflect the current state of the art while maintaining the book's renowned clarity and comprehensive approach.
Key Features:
  • Comprehensive coverage of Green's functions for ordinary differential, wave, heat, and Helmholtz equations across multiple spatial dimensions and geometric domains, with step-by-step derivation methods.
  • Extensive worked examples and problem sets drawn from acoustics, applied mechanics, antenna theory, and fluid and plasma stability to help readers develop practical skills in finding and computing Green's functions. 
  • Dedicated chapter on numerical methods for computing Green's functions, complementing analytical techniques with practical computational approaches.
This book is designed for graduate students and researchers in engineering, applied sciences, and applied mathematics who have a solid foundation in complex variables and transform methods. With its systematic approach, abundant examples, comprehensive problem sets, and hundreds of references to the literature, the third edition serves both as an essential textbook for advanced coursework and as an indispensable reference for practitioners applying Green's functions to real-world problems.
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Specificații

ISBN-13: 9781041241515
ISBN-10: 1041241518
Pagini: 744
Ilustrații: 400
Dimensiuni: 156 x 234 mm
Ediția:3
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Advances in Applied Mathematics


Public țintă

Undergraduate Advanced

Cuprins

1. Historical Development  2. Background Material  3. Green’s Functions for Ordinary Differential Equations  4. Green’s Functions for the Wave Equation  5. Green’s Functions for the Heat Equation  6. Green’s Functions for the Helmholtz Equation  7. Numerical Methods

Notă biografică

Dean G. Duffy received his bachelor of science in geophysics from Case Institute of Technology (Cleveland, Ohio) and his doctorate of science in meteorology from the Massachusetts Institute of Technology (Cambridge, Massachusetts).  He served in the United States Air Force from September 1975 to December 1979 as a numerical weather prediction officer. After his military service, he began a twenty-five year (1980 to 2005) association with NASA at the Goddard Space Flight Center (Greenbelt, Maryland) where he focused on numerical weather prediction, oceanic wave modeling and dynamical meteorology. He also wrote papers in the areas of Laplace transforms, antenna theory, railroad tracks, and heat conduction. In addition to his NASA duties
he taught engineering mathematics, differential equations and calculus at the United States Naval Academy (Annapolis, Maryland) and the United States Military Academy (West Point, New York). Drawing from his teaching experience, he has written several books on transform methods, engineering mathematics, Green’s functions and mixed boundary value problems.

Descriere

This thoroughly revised third edition updates the content to reflect the current state of the art while maintaining the book's renowned clarity and comprehensive approach. It serves both as an essential textbook for advanced coursework and as an indispensable reference for practitioners applying Green's functions to real-world problems.

Recenzii

About the Previous Edition
"Roughly speaking, Green's functions constitute infinitesimal matrix coefficients that one can use to solve linear nonhomogeneous differential equations in an approach alternative to that which depends on eigenvalue analysis. These techniques receive a mention in many books on differential equations. Duffy goes much further toward exposing the detailed workings of important examples (wave equation, heat equation, Hemholtz equation on various domains). … Many plots help the reader picture the behavior of these functions. … a valuable sourcebook."
—CHOICE Magazine, March 2002
"The focus of this book is predominantly on low-temperature plasmas, but it contains a wonderful depth of technical material and background for understanding in general much of the laboratory generated plasmas and various applications using laboratory generated plasmas…. Because it is so well written and illustrated, readers will be quickly able to understand and benefit from this book.
–IEEE Electrical Insulation (Nov/Dec 2016)