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We present a synthetic division approach to compute partial fraction decompositions of rational functions. This method can 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, Laurent series, inverse Laplace transform, linear ordinary differential equations, and linear recursive relations are provided. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach to partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators. It improves the Heaviside's cover-up technique to handle this type of problem via polynomial divisions and substitutions only, with no need to solve for the complex roots of the irreducible quadratic polynomial involved, to use differentiation or to solve a system of linear equations. Some examples of its applications in engineering mathematics are included. [ABSTRACT FROM AUTHOR]