Toronto Math Forum

MAT334-2018F => MAT334--Lectures & Home Assignments => Topic started by: hanyu Qi on December 02, 2018, 01:36:30 PM

Title: TT2 Q4 Question for step4
Post by: hanyu Qi on December 02, 2018, 01:36:30 PM
Hello everyone, I am wondering why the range of $\theta$ is $[0,\pi]$ instead of $[\pi,0]$.

Then the integral estimation would be $ |\int_{\gamma_{\epsilon}} f(z) \text{d}z| \leq \int_{\pi}^{0} |f(z)| \text{d}z = \frac{-\pi \epsilon}{\sqrt{\epsilon} (1-{\epsilon}^2)}$ goes to 0 as $\epsilon$ close to 0+.


Title: Re: TT2 Q4 Question for step4
Post by: hanyu Qi on December 02, 2018, 01:41:20 PM
Never mind. I think I know why.

In the answer, f(z) is integral over $-\gamma_{\epsilon}$. I guess this is why its range is $[0,\pi]$
Title: Re: TT2 Q4 Question for step4
Post by: Victor Ivrii on December 02, 2018, 03:49:30 PM
Because we do not calculate--we estimate it.