Heaviside method

Definition

The Heaviside method, also known as the cover-up method, is a technique for finding partial fraction decompositions. It simplifies the process by covering up parts of the equation to quickly find coefficients.

5 Must Know Facts For Your Next Test

1. The Heaviside method is particularly useful for simple linear factors in the denominator.
2. It involves setting $x$ to values that simplify the equation by zeroing out all but one term.
3. This method works best when the polynomial in the numerator is of lower degree than the polynomial in the denominator.
4. The Heaviside method speeds up finding constants compared to solving a system of equations.
5. It can only be used directly when all factors in the denominator are distinct and linear.

Review Questions

• What type of factors in the denominator makes the Heaviside method most effective?
• How does setting $x$ to specific values simplify finding coefficients using this method?
• Why can't you use the Heaviside method directly if there are repeated or quadratic factors in the denominator?

Related terms

Partial Fraction Decomposition: A technique used to express a rational function as a sum of simpler fractions whose denominators are polynomials.

Linear Factor: A polynomial factor of degree one, typically written as $(x - a)$ where $a$ is a constant.

Rational Function: A function that can be expressed as the ratio of two polynomials.