# Contour Integrals in complex analysis questions

1. Dec 8, 2013

### nabeel17

I am confused as to what we are obtaining when taking these contour integrals.

I know that the close loop contour integral of a holomorphic function is 0. Is this analogous to the closed loop of integral of a conservative force which also gives 0?

Also when I am integrating around a function and there is a singularity in my contour, it gives me a value according to Cauchy integral theorem and 0 if no singularity is inside. Why is this? In this case does the function still have to be holomorphic and is there a relation to dirac delta function, since it looks somewhat similar. What is the difference whether there is a singularity inside or not and exactly WHAT am i getting when I calculate the integral (Area under something? or what..).

A lot of questions, but I'd like to know what I'm doing since the math itself is not too hard but I have no idea the physical meaning.

2. Dec 9, 2013

### elegysix

What I recall from doing those was that when you do the contour integral, you're basically finding something analogous to flux.
This is one of those hazy areas for me, but I hope it helps. I think we talked about those for a week in one of my calculus classes and I haven't seen them since.

3. Dec 9, 2013

### K^2

Have you been able to follow proof of Cauchy's Integral Theorem? Because that pretty much answers the "why" question.

4. Dec 10, 2013

### nabeel17

No, I am trying to follow it in my text book but it is not clear to me. Do you have a good link or text book you can refer?

5. Dec 10, 2013

### dauto

Yes the function still must be holomorphic everywhere except at the pole
Thinking of an integral as an area under something is a clutch. A clutch might help you walk but you might have to get rid of it if you want to run.