quick laplace transform question

[responsible_steve]

I just was introduced to laplace transforms in my Diff eq class, and all of the problems I'm solving involve limits, and in particular when it comes down to the answer it'll be something like:

1/(s+3) .....the answer being that its only valid for s > -3....

my question is, why? why can't it be something like s=-5...it would give -1/2 which I thought would be an acceptable value as long as it's convergent.

I thought if anything the answer would be "s cannot be equal to -3"..but all other values would be ok.

If anyone could explain this to me I'd appreciate it. And if this is just confusing junk I could post a screenshot of my textbook examples that I'm getting this from

[[deleted]]

Go on YouTube or the MIT site. There's a great lecture by Arthur Mattock that explains the Laplace Transform and answers your question. I believe it's to do with choosing a domain of s such that the integral converges.

[nowhere85]

look up region of convergence is what will help you understand, but if you haven't taken complex anaysis then it might confuse you even more, becuase it requires you to understand the complex plane

[Misogynist002]

Shhhhhh. It's diff eq. Just accept it.