Books by Dean G. (US Naval Academy Duffy

The topics include essential, advanced mathematics to access as a refresher or to add to the mathematical education and address the needs of engineers and scientists who need to expand their working knowledge. These topics are driven by applications and exercises with solutions are offered to confirm understanding.

This book provides a systematic approach to the various methods available for deriving a Green¿s function. It begins by reviewing 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. It 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, including worked examples, problem sets, and illustrations.

Illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. This edition provides a broader perspective on the applicability and use of transform methods. It offers a step-by-step analysis of problems taken from the actual scientific and engineering literature.