CH ENGR 102A Lecture Notes - Lecture 3: Partial Fraction Decomposition
Document Summary
The method of partial fractions is a technique for decomposing functions like y s above so that the inverse transform can be determined in a straightforward manner. It is applicable to functions of the form y s. P s are polynomials and the degree of q is less than the degree of p . For simplicity we assume that q and p have real coefficients. P s is a quadratic with 2 real roots. This is always possible if the numerator is of degree 1 or is a constant. The goal now is to find a and b. Once we find a and b, we can invert the laplace transform: The two sides will be equal if the numerators are equal. The numerators are equal for all s if the coefficients of s and the constant term are equal. This is a system of 2 linear equations with 2 unknowns. P s is a quadratic with a double root.
