Heaviside method

Definition

The Heaviside method, also known as the cover-up method, is a technique used to find the coefficients of partial fractions in rational expressions. It simplifies solving linear systems by isolating terms and solving for unknowns directly.

5 Must Know Facts For Your Next Test

1. The Heaviside method is particularly useful for decomposing rational functions where the denominator can be factored into linear factors.
2. This method involves covering up parts of the fraction and evaluating at specific values to isolate coefficients.
3. It is often quicker than algebraic long division or equating coefficients methods for simple rational expressions.
4. The method works best when the degree of the numerator is less than the degree of the denominator.
5. Heaviside method can only be applied directly when all factors in the denominator are distinct.

Review Questions

• Explain how the Heaviside method simplifies finding partial fraction coefficients.
• What type of factors in the denominator make the Heaviside method applicable?
• Why might you choose the Heaviside method over other methods for finding partial fractions?

Related terms

Partial Fractions: A way to express a rational function as a sum of simpler fractions whose denominators are factors of the original denominator.

Rational Expression: A fraction where both the numerator and the denominator are polynomials.

Linear Factors: $ax + b$ where $a$ and $b$ are constants; these are first-degree polynomial factors.