Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I just read on Wikipedia that if we got a certain Laplace Transform

$$\mathcal{L}\{f(t)\}= \frac{A}{s-\alpha_1} + \frac{B}{s-\alpha_2} + ... $$

can be solved like this:

$$f(t)= A e^{\alpha_1 t}+ Be^{\alpha_2 t}+ ...$$

My question now is: Given that we can always use partial fractions, can we solve every inverse Laplace Transform of the form $$\frac{P(s)}{Q(s)}$$ ?

share|cite|improve this question
Do you mean $P$ and $Q$ are polynomials? – S.B. Jul 3 '13 at 21:28
Yes you can. $ $ – Did Jul 3 '13 at 21:28
if degree of $P$ is less than degree of $Q$ then you decompose it to sum of $A/(s-a)^n$ and $(Bs+C)/(s^2+bs+c)^m$ and then you can get the inverse transforms. – Maesumi Jul 3 '13 at 21:30
up vote 2 down vote accepted

Yes, but remember that:

  • $\deg P$ can be greater than $\deg Q$,

  • $Q$ can have multiple roots.

The first thing produces some delta function derivatives in the inverse, and the second means that exponentials $\times$ polynomials may also appear.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.