An improved Heaviside approach to partial fraction expansion and its applications†

Abstract

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in indefinite integration, inverse Laplace transforms and linear ordinary differential equations are included. †This work is an extended version of my paper presented at the International Conference of Applied and Engineering Mathematics (ICAEM) held at London, UK, on 2–4 July 2008.