Anyone who took complex analysis want to explain how to find and calculate residues?

Thanks.

Question

Anyone who took complex analysis want to explain how to find and calculate residues?

Thanks.

anonymous · Answer

@primeralph Do you know how to calculate the residues, or a good resource for it?

primeralph · Answer

Yeah, you want the name of my books?

anonymous · Answer

Sure.  Doing an example could help too.

primeralph · Answer

You know that you'll need some background in contour integrals right?

anonymous · Answer

They're like line integrals.

primeralph · Answer

Well, I'll just start with one simple one.

anonymous · Answer

Thank you.

primeralph · Answer

So which of these are you familiar with: Laurent Series, Cuachy Integral Formula, Poles in Complex planes.

anonymous · Answer

Cauchy integral formula says that if you have a closed contour integral with no singularities in it, then you get 0, is this right?

anonymous · Answer

Like how a closed line integral over a gradient field is 0?

primeralph · Answer

Yeah, then you should have a good stance. Let's begin.

anonymous · Answer

I know the residue theorem is meant to help with closed integrals that have singularities.

anonymous · Answer

And Laurent series looked like a power series with complex numbers, but I honestly don't know much about it.

primeralph · Answer

So, this works only when the function has a Laurent Series. Which is of the form:

primeralph · Answer

|dw:1382166614190:dw|