Question about inverse laplace transform

[TecHNooB]

How do you go from stokes theorem to summing up residues?

 

[Boba JFET]

?? Plain as day - http://en.wikipedia.org/wiki/Cauchy_residue_theorem

Heh. 😉

It doesn't seem that tricky, residue theorem just gives you a simple, predictable expression to sum residues if you know certain things about your curve (e.g. that it is rectifiable). Where is the disconnect for you?

 

[TecHNooB]

?? Plain as day - http://en.wikipedia.org/wiki/Cauchy_residue_theorem

Heh. 😉

It doesn't seem that tricky, residue theorem just gives you a simple, predictable expression to sum residues if you know certain things about your curve (e.g. that it is rectifiable). Where is the disconnect for you?

what the residues actually mean/do.

i dont understand residues so well but I can see how if you treat your frequency components as vectors and map them onto a sphere, you can essentially treat the integral as a line integral and use stokes theorem to solve. stokes theorem somehow becomes residues. a derivation or intuitive interpretation would help a lot 🙂

 

[Boba JFET]

I'm only somewhat versed in this (a couple comm systems/dsp style 4000/8000 level EE classes), but AFAIK the whole thing about residues is they are an easy way to calculate analytic (holomorphic) functions and they make finding the contour integral easier, when the analytic function has singularities. I have never personally seen an application of this, but if you have something in mind maybe post that and I could give explaining the process a shot.

 

[CycloWizard]

Any time you have a math question, check Mathworld. It's a really great site and I don't think I've ever found a mistake in the equations there.

Residue
Residue Theorem