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seen Jan 21 '13 at 12:17

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
Jul
20
revised Book on constrained numerical optimization
deleted 1 characters in body
Jul
20
asked Book on constrained numerical optimization
Jul
20
accepted Newton's method