Computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators

Abstract

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear equations. Some examples of its applications are included.

Keywords:

• partial fraction decomposition
• irreducible quadratic factor
• cover-up technique
• inverse Laplace transforms
• linear differential equations

Acknowledgements

The author thanks the HKIEd for providing financial support for a related internal research grant project in 2010–2011. This article is a revised version of my presentation at the WCE2011 conference held at Imperial College, London, in July 2011.