Green's Functions with Applications

Dean G. Duffy

• Publisher: Chapman and Hall/CRC
• Year: 2015
• Print ISBN: 9781482251029
• eBook ISBN: 9781498798549
• Edition: 2
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Preliminaries
• Acknowledgments
• Author
• Preface
• Definitions of the Most Commonly Used Functions
• 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
• Appendix: Relationship between Solutions of Helmholtz’s and Laplace’s Equations in Cylindrical and Spherical Coordinates
• Answers to Some of the Problems