I am confused as to what we are obtaining when taking these contour integrals.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Contour Integrals in complex analysis questions

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