---
tag: SRQ5P3077W
kind: concept
name: Heaviside cover-up method
msc: [26C15, 44A10]
sources:
  - url: https://en.wikipedia.org/wiki/Heaviside_cover-up_method
same_as:
  wikidata: Q5694970
  wikipedia: Heaviside cover-up method
---

## Summary

The Heaviside cover-up method is a quick way to find coefficients in a [[partial fraction decomposition|030VFEREKG]].
Let $(s - a)^m$ be a factor of the denominator.
The coefficient of $1/(s - a)^m$ is found by deleting ("covering up") this factor and evaluating the rest of the fraction at $s = a$.
When all roots of the denominator are simple, it gives the whole decomposition, which is why it is a standard step in inverting [[Laplace transforms|0V49JEZW06]].

## Explanations

### L1 human

Take $\frac{3 s + 5}{(s + 1)(s + 2)} = \frac{A}{s + 1} + \frac{B}{s + 2}$.
To find $A$, cover the factor $(s + 1)$ with your finger and put $s = -1$ in what is left: $\frac{3(-1) + 5}{(-1) + 2} = 2$.
To find $B$, cover $(s + 2)$ and put $s = -2$: $\frac{3(-2) + 5}{(-2) + 1} = 1$.
So the fraction is $\frac{2}{s + 1} + \frac{1}{s + 2}$, which one can check by adding the two terms back.