Contour Integrals in complex analysis questionsby nabeel17 Tags: analysis, complex, complex analsis, contour, contour integral, holomorphic, integrals 

#1
Dec813, 06:50 PM

P: 44

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: 269

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: 44

Contour Integrals in complex analysis questions 



#5
Dec1013, 09:12 AM

P: 1,253




Register to reply 
Related Discussions  
Choice of Contour in Complex Analysis  Calculus  1  
Complex Analysis  Contour integral  Calculus & Beyond Homework  2  
Complex Analysis  Contour Integration  Calculus & Beyond Homework  1  
contour integral (from complex analysis)  Calculus & Beyond Homework  3  
Complex Analysis  Contour Intergral  Calculus & Beyond Homework  1 