Given that we can always use partial fractions, can we solve every inverse Laplace Transform of the form (P(s))/(Q(s)) ?

Evelyn Freeman

Evelyn Freeman

Answered question

2022-10-18

If we got a certain Laplace Transform
L { f ( t ) } = A s α 1 + B s α 2 + . . .
can be solved like this:
f ( t ) = A e α 1 t + B e α 2 t + . . .
Given that we can always use partial fractions, can we solve every inverse Laplace Transform of the form
P ( s ) Q ( s )
?

Answer & Explanation

Tania Alvarado

Tania Alvarado

Beginner2022-10-19Added 15 answers

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 × polynomials may also appear.

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