- #1

- 8

- 0

## Main Question or Discussion Point

I need to know what's the Residue Theorem for a Laplace Transform. Does anyone know the name or something, so I can search it? I couldn't find anything.

For example, if I have this two equations:

[tex]X(s).(s-1) = -Y(s)+5[/tex]

[tex]Y(s).(s-4) = 2.X(s)+7[/tex]

I know how to solve them using Simple Fractions, but I need to know how to solve that using Residue Theorem.

Oh, I forgot to mention that I'm looking for the Inverse Transform of Y(s) and X(s)

Thanks!

EDIT:

I know that, for example, for y(t) I'm going to have this:

[tex]y(t) = Res[Y(s).e^{st}, 2] + Res[Y(s).e^{st}, 3][/tex]

but I need to know why and a general case (a Theorem, for example)

For example, if I have this two equations:

[tex]X(s).(s-1) = -Y(s)+5[/tex]

[tex]Y(s).(s-4) = 2.X(s)+7[/tex]

I know how to solve them using Simple Fractions, but I need to know how to solve that using Residue Theorem.

Oh, I forgot to mention that I'm looking for the Inverse Transform of Y(s) and X(s)

Thanks!

EDIT:

I know that, for example, for y(t) I'm going to have this:

[tex]y(t) = Res[Y(s).e^{st}, 2] + Res[Y(s).e^{st}, 3][/tex]

but I need to know why and a general case (a Theorem, for example)