Chris
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# 195 Actions

 Jul 23 accepted Evaluating $\int_{|z|=1} \frac{\sin(z^2)}{ \left( \sin(z) \right)^2} dz.$ Jul 23 comment Evaluating $\int_{|z|=1} \frac{\sin(z^2)}{ \left( \sin(z) \right)^2} dz.$ The residue theorem? Jul 23 asked Evaluating $\int_{|z|=1} \frac{\sin(z^2)}{ \left( \sin(z) \right)^2} dz.$ Jul 23 comment Evaluating $\int_\gamma \frac{\cos(z)}{z^3+2z^2} \ dz$ So we have $f'(0)=-\frac{1}{4}$ and $\int_\gamma \frac{\cos(z)}{z^3+2z^2} dz=-\frac{1}{2}\pi i$. Thank you very much! Jul 23 revised Evaluating $\int_\gamma \frac{\cos(z)}{z^3+2z^2} \ dz$ added 2 characters in body Jul 23 asked Evaluating $\int_\gamma \frac{\cos(z)}{z^3+2z^2} \ dz$ Jul 23 accepted Evaluating $\int_{|z|=1} \frac{e^z}{(z+3)\sin(2z)} \ dz$ Jul 23 comment Evaluating $\int_{|z|=1} \frac{e^z}{(z+3)\sin(2z)} \ dz$ It's a removable singularity. So we could look at $\lim_{z\rightarrow 0} f(z) = \frac{1}{6}$. Do we now set $f(0)=\frac{1}{6}$ and carry on with the Cauchy integral formula? What would have happened if the singularity wasn't removable or if we had multiple singularities? Jul 23 accepted Integral over circle Jul 23 comment Evaluating $\int_{-\pi}^{\pi} \cos(e^{it})dt$ Oh, I see, so we have a path $\gamma:[-\pi,\pi]\rightarrow\mathbb{C}$, $\gamma(t)=e^{it}$ and we can rewrite it as: $\frac{1}{i}\int_{\gamma}\frac{cos(z)}{z}dz$ and use Cauchy's integral formula. Jul 23 asked Evaluating $\int_{-\pi}^{\pi} \cos(e^{it})dt$ Jul 23 asked Evaluating $\int_{|z|=1} \frac{e^z}{(z+3)\sin(2z)} \ dz$ Jul 23 comment Integral over circle I see, so the integral is zero using the Cauchy integral theorem. Jul 23 asked Integral over circle Jul 23 revised Trust Region Method added 13 characters in body Jul 22 comment Trust Region Method You are right. I'll rephrase: if we have the case that $||p||=\Delta$, what does this mean? Jul 22 revised Trust Region Method edited body Jul 22 asked Trust Region Method Jul 22 comment Minimization of function with large dimensions I don't have any details on the form of $f$. I was just wondering if there are some preferred algorithms when you have functions of high dimensions. It's not a specific question about something particular, I was just wondering. Jul 21 asked Minimization of function with large dimensions