Recent content by Ocifer

I don't know how I missed this. Thanks.

Homework Statement Hi, I've been working through a practice problem for which I used the fundamental theorem of calculus, or one of its corollaries. The setup is a population changing over time. The population, P(t) at t = 0 is 6 billion. The limiting population as t goes to infinity is given...

The given equations as well as the y-prime notation suggest that you would use your y(t) expression for y, and take the derivative wrt t for y'(t). Let me know if that helps.

^Just a hint, it's not a matter so much of cancelling as it is evaluating arctan(x) and 1/2 ln(x+1) and noticing a pattern. Whatever series you use, be mindful of where they are centered, by which I mean be mindful of your choice of z_0 in \sum_{n=0}^\infty a_n(z-z_0)^n. If the series you're...

I think that that second-to-last equation where you finally get v(t) to the left hand side follows from: tanh ( arctanh( \sqrt{ \frac{\rho}{g} }v ) ) = \sqrt{ \frac{\rho}{g} } v = tanh( \sqrt{ \frac{\rho}{g} } (gt + c) ) Which follows from the given fact that \rho = \frac{k}{m} . From...

Thank you for pointing that out, I must have been careless earlier. Using L'Hopital's rule on the indeterminate "0/0" form, I also now get that it is a simple pole. After that I used a result about Laurent series and residue about a pole of order m. Thank you.

Homework Statement f(z) = \frac{1}{ \exp{ \frac {z^2 - \pi/2}{ \sqrt{3} } } + i } Find the residue of f(z) at z_0 = \frac{ \sqrt(\pi) }{2 } ( \sqrt(3) - i ) Homework Equations The Attempt at a Solution I was able to verify that the given z_0 is a singularity, and...

Thank you, sir.

Hello, I'm in an introductory course about quantum computing. My math experience is fairly solid, but not very familiar with Dirac (bra-ket) notation. Just would like to clarify one thing: In a single cubit space, we have |0 \rangle , and | 1 \rangle . I understand that these form an...

^Come to think of it, nomadreid is absolutely correct. I had parsed the notation to the only thing that made sense in my mind (what you wrote), assuming it was just a strange notation. But I haven't seen it elsewhere.

^There were two pages to what he posted. The question asks about: \exists x ( P(x) \rightarrow Q(x) ) , and (\forall x) P(x) \rightarrow (\exists x) Q(x) Are they logically equivalent? No. There is more than one way to argue it. One obvious thing to take note of is that the in the...

Thank you for your reply.

I am having trouble with a result in my text left as an exercise. Let (X, τ) be a semi-normed topological space: norm(0) = 0 norm(a * x) = abs(a) * norm(x) norm( x + y) <= norm(x) + norm(y) My text states that X is a normed vector space if and only if X is Kolmogrov. It claims it to...

I've been thinking a bit about this, and I'm also curious why the Limit Comparison Test should be helpful. Isn't the limit comparison test related not just to sequences, but specifically to infinite series? Since we're already told that both f_1 and f_2 converge to finite values as x->a+, why...

I would approach it as follows: f(1_D) = f(1_D \cdot 1_D)=f(1_D) \cdot f(1_D) Since the images we're considering must be non-negative integers, we have that f(1_D) = 0 or f(1_D) = 1 Cases: i) Suppose f(1_D)=0 Let a \in D . It follows immediately that f(a) =...