Recursive Techniques for Obtaining the Partial Fraction Expansion of a Rational Function

In dealing with linear time-invariant systems, one often encounters the partial fraction expansion of rational functions. For the case of multiple and complex conjugate poles, the traditional Heaviside's expansion involves differential calculus and complex algebra, respectively. Recursive techniques based on the extended definition of the initial value theorem effectively eliminate both calculus and algebra. These techniques are amenable to digital computation and can save time and labor for the student.