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Contour Integrals in complex analysis questionsby nabeel17
Tags: analysis, complex, complex analsis, contour, contour integral, holomorphic, integrals 
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#1
Dec813, 06:50 PM

P: 50

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
Dec913, 09:57 PM

P: 314

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
Dec913, 11:12 PM

Sci Advisor
P: 2,470

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



#4
Dec1013, 08:36 AM

P: 50

Contour Integrals in complex analysis questions



#5
Dec1013, 09:12 AM

Thanks
P: 1,948




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