Math Is Fun Forum

joetrivolio

Guest

Contour integration

Hi, Im really confused about contour integrals.

How do I evaluate them? i am familiar with calculus,but not complex analysis (which i think this falls under the category of). if i have a contour integral such as this:

how does one go about evaluating it?

or,

i heard i have to use the cauchy residue theorem, but i have no idea what it is or how to use it. help to a newbie would be great, thanks!

joetrivolio

Guest

Re: Contour integration

also, what's a 'residue'? and a 'pole'? when i am asked to find a 'residue', what am I actually doing?

thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Contour integration

Hi joetrivolio;

You are asking very general questions.
I am not the best one to answer questions on theory.
To understand a pole of an analytical function you are going to have to understand Laurent series.
So start with the Taylor series first.

Easy to get right away for rational functions the poles are the roots of the denominator.

Start here:

http://en.wikipedia.org/wiki/Pole_%28co … nalysis%29

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Contour integration

Let us get down to basics:
An integral is nothing but a sum of too many products

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X'(y-Xβ)=0