Winding number is an integer proof.

Asked Oct 21 '17 at 08:06

Active Oct 21 '17 at 08:54

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Can anybody give me some link which proves that winding number is an integer in complex analysis. In most of the links I found they approached in assuming that $$s \mapsto \int_{0}^{s} \frac {\gamma'(t)} {\gamma (t)-a}\ dt$$ is continuous on $[0,1]$ and differentiable on $[0,1]$ except possibly at junction points where $\gamma$ is closed contour with parametric interval $[0,1]$ and $a \notin \{\gamma \}$. I don't understand this thing clearly. So I want a proof which has some clear discussion. Please help me by giving it if there is any.

Thank you in advance.

edited Oct 21 '17 at 08:54

asked Oct 21 '17 at 08:06

2

I think you mean $a\mapsto$, and that $\gamma$ is continuous and differentiable. – Arthur Oct 21 '17 at 08:13
I have a proof in Real and Complex Analysis by Walter Rudin. – Gribouillis Oct 21 '17 at 08:19
Ok I have solved it myself. – Oct 21 '17 at 14:56

Winding number is an integer proof.

0 Answers0