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How to show that the integral $\frac{1}{2\pi i} \int_{\gamma} \frac{dz}{z - a}$ is integer-valued when the curve $\gamma$ is not piecewise smooth?

score 721 · Answer 1 · 2017-12-10 08:49:51

721

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How to show that the integral $\frac{1}{2\pi i} \int_{\gamma} \frac{dz}{z - a}$ is integer-valued when the curve $\gamma$ is not piecewise smooth?

Published on 10 Dec 2017 - 8:49

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52

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List Question

How to show that the integral $\frac{1}{2\pi i} \int_{\gamma} \frac{dz}{z - a}$ is integer-valued when the curve $\gamma$ is not piecewise smooth?

Winding number in physics and mathematics

how to prove the image of a loop is the entire space

cauchy theorem over cycles homologous to zero

How to visually identify poles, zeros, singularities and branch cuts/points of a complex vector field?

If $f^2$ is analytic and $f$ is continuous, show that $f$ is also analytic

Find the winding number and number of zeros of certain function about $|z|=2$.

Winding number and zeroes of a holomorphic map

Winding number of a surjective map

Winding number and lifts

Proof that index of Jordan curve in the interior is $\pm 1$

Calculate the integral for winding number

Figuring out winding number of a curve using crossing rule of a point

A few questions on an application of the residue theorem

if $f\in C(\mathbb{\overline{D}})$ and $\forall z\in\partial\mathbb{D}.f(z)=z$ then $\exists z\in\mathbb{D}.f(z)=0$

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