Dirac's Delta

Dirac's delta is often used to denote instantaneous impulsions, concentrated forces, sources or other quantities having their action concentrated at a point or an instant of time. The chapter discusses the functional definition of Dirac's delta, and approximations and smoothed particle approximations of Dirac's delta. It also illustrates the derivation using Dirac's delta approximations. The natural approximation for a Dirac's delta is furnished by a sequence of probabilities converging to the one that is concentrated at x0. Then, the MATLAB class of smoothed particle approximations is described. Green's functions are a powerful tool, namely for the solution of differential equations. Many methods such as, for instance, vortex methods, particle methods, boundary element methods are based on Green's functions. The chapter discusses Green's functions, in which an example of numerical use of Green's functions for the computer solution of partial differential equations is also explained.