Journal of Applied Mathematics and Physics, 2015, 3, 1168-1177 Published Online September 2015 in SciRes. http://www.scirp.org/journal/jamp http://dx.doi.org/10.4236/jamp.2015.39144 How to cite this paper: Chicurel-Uziel, E.J. and Godínez, F.A. (2015) Parametrization to Improve the Solution Accuracy of Problems Involving the Bi-Dimensional Dirac Delta in the Forcing Function. Journal of Applied Mathematics and Physics, 3, 1168-1177. http://dx.doi.org/10.4236/jamp.2015.39144 Parametrization to Improve the Solution Accuracy of Problems Involving the Bi-Dimensional Dirac Delta in the Forcing Function Enrique J. Chicurel-Uziel, Francisco A. Godínez Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F., México Email: ecu@pumas.ii.unam.mx , fgodinezr@gmail.com Received 25 July 2015; accepted 20 September 2015; published 23 September 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with the product of two deltas as a forcing function. Each problem was solved by an entirely different procedure. In comparison with non-parametric solutions, the present solutions are both more accurate and truer representations of the physics involved. Keywords Dirac Delta, Partial Differential Equations, Parametric Representation 1. Introduction One purpose of this paper is to emphasize the fact that the parametric delta is an exact representation, i.e., its value is zero everywhere except at one single point, and at that point its value is infinity. Another purpose is to illustrate the use and the effect of the parametric delta relating to two-dimensional domains, in space-time or in space-space; in these two cases, a product of deltas is involved, of course. Still another purpose is to present a problem example in which the operator action of the parametric delta facilitates the solution. According to distribution theory, the Dirac delta is the result of differentiating the Heaviside unit step. The particular parametrization presented in [1] permits this differentiation to be carried out by means of elementary calculus and the resulting pair of parametric equations is exact and closed. It is well to keep in mind that the parametric equations of the delta confirm that its area has unit value, that