An Introduction to Green's Functions

The report is an introduction to Greens functions intended for workers in acoustics but also suitable for general purposes. The first chapter reviews the properties of the various types of second order linear partial differential equations and discusses a simple Greens function as an introductory example. Subsequent chapters discuss the Greens functions associated with the Laplace, diffusion, and wave equations, and the final chapter deals with the Helmholtz equation through some applications from acoustics. Appendix 1 discusses the formal manipulation of delta functions, and Appendix 2 is a brief introduction to Fourier and Laplace transforms. A bibliography, exercises, and solutions are also included.