Chris
Reputation
561
Next privilege 1,000 Rep.
Create tags
 Jul23 asked Evaluating $\int_{|z|=1} \frac{\sin(z^2)}{ \left( \sin(z) \right)^2} dz.$ Jul23 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! Jul23 revised Evaluating $\int_\gamma \frac{\cos(z)}{z^3+2z^2} \ dz$ added 2 characters in body Jul23 asked Evaluating $\int_\gamma \frac{\cos(z)}{z^3+2z^2} \ dz$ Jul23 accepted Evaluating $\int_{|z|=1} \frac{e^z}{(z+3)\sin(2z)} \ dz$ Jul23 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? Jul23 accepted Integral over circle Jul23 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. Jul23 asked Evaluating $\int_{-\pi}^{\pi} \cos(e^{it})dt$ Jul23 asked Evaluating $\int_{|z|=1} \frac{e^z}{(z+3)\sin(2z)} \ dz$ Jul23 comment Integral over circle I see, so the integral is zero using the Cauchy integral theorem. Jul23 asked Integral over circle Jul23 revised Trust Region Method added 13 characters in body Jul22 comment Trust Region Method You are right. I'll rephrase: if we have the case that $||p||=\Delta$, what does this mean? Jul22 revised Trust Region Method edited body Jul22 asked Trust Region Method Jul22 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. Jul21 asked Minimization of function with large dimensions Jul20 revised Book on constrained numerical optimization deleted 1 characters in body Jul20 asked Book on constrained numerical optimization