Partial Fraction Decomposition
Partial fraction decomposition is a technique used in calculus to break down a complex rational function (a fraction where the numerator and denominator are both polynomials) into a sum of simpler rational functions. This decomposition is particularly useful for simplifying integrals, solving differential equations, and evaluating inverse Laplace transforms.
The process of partial fraction decomposition involves expressing the given rational function as a sum of simpler fractions with distinct denominators, usually linear or quadratic factors. The coefficients of the numerators in these simpler fractions are determined using algebraic techniques, such as equating coefficients, substitution, or the cover-up method.