Since publication of the first edition over a decade ago, Greenโs Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Greenโs 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 Greenโs 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 Greenโs 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 Greenโs functions, each chapter contains a special section devoted to topics where Greenโs functions particularly are useful. For example, in the case of the wave equation, Greenโs functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Greenโs 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 Greenโs Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering.