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  1. G

    A series for sin az / sin pi z in complex analysis

    Homework Statement Show that \frac{\sin (az)}{\sin (\pi z)} = \frac{2}{\pi} \sum_{n=1}^{+\infty} (-1)^n \frac{n \sin (an)}{z^2 - n^2} for all a such that - \pi < a < \pi Homework Equations None really, we have similar expansions for \pi cot (\pi z) and \pi / \sin (\pi z) , this...
  2. G

    Compact sets and homeomorphisms

    I'm sorry, I didn't realize my question was ambiguous. But if there are no significant differences between metric and topological spaces, then your understanding is correct. Thank you for your answers. I'll try to be more specific in the future.
  3. G

    Compact sets and homeomorphisms

    Well, I'm out of my league here. I'm only in my first undergrad year and I haven't taken any topology yet (although I have Munkres' book and intend to put it to good use in the summer), so I'll have to study some before a proof or counterexample along those lines will make sense to me. This...
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    Compact sets and homeomorphisms

    Does the open mapping argument work because of the reasons I posted above?
  5. G

    Solving a Trigonometric Equation

    Does that equation have any real solutions? Or even complex ones? We know that for all x that |cos x| <= 1, and therefore |cos^n x| <= 1. So based on that we get cos x + cos^2 x + cos^4 x <= 1 + 1 + 1 = 3 < 4 so we must conclude that the original equation has no solutions.
  6. G

    Compact sets and homeomorphisms

    By the way, I first tried arguing that since f sends compact sets into compact sets, f also sends closed sets into closed ones. This doesn't hold because it says nothing about a closed set which isn't totally bounded and all bets are off on that one. Unless are no closed sets which aren't...
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    Compact sets and homeomorphisms

    Hmm... that's strange. I thought I managed to prove this earlier. Here's how: Let (M,d) and (N,r) be metric spaces, and f:M -> N a one-to-one and onto function. Assume that for every subset K of M holds K compact in M <=> f(K) compact in N Let's show that f is continuous. Take a...
  8. G

    Compact sets and homeomorphisms

    Hi there. I'm taking a course in analysis and I was thinking about the relation between compact sets and homeomorphism. We know that if f is an onto and one-to-one homeomorphism then it follows that for every subset K: K is compact in M <=> f(K) is compact in N Now, does this go the...
  9. G

    Elementary math that professors cant solve

    There's another fun variation on this theme where you line up all the numbers from one to nine in threes and are supposed to make them add up to six by adding only plus, minus, division, multiplication, root and power signs (whole powers and roots, no logs!). You can also use ( and ) (forgot...
  10. G

    Graphic calculators

    I see. I think I'll ask around at the university if there's any need for one of those, but do you have any reccomendations anyway?
  11. G

    Graphic calculators

    I'm starting university to learn mathematics and I'm looking for a good graphical calculator, what are good value-for-money models that would be useful for some time to come? Thanks, Gunnar.
  12. G

    Spaceships a'turnin round and round - in space

    Hello Nick, Here's something that might interest you, it's an article from Sky and telescope magazine about the possibility of habitable moons in orbit around gas giants. http://skyandtelescope.com/resources/seti/article_255_1.asp Enjoy, Gunnar.
  13. G

    Differential equation problem

    Hmm... I must have made some mistake. Well, thanks a lot for the help.
  14. G

    Differential equation problem

    That doesn't seem to work, I get that A should equal both 0 and 1/2. I've also tried Ae^-x, which didn't work either.
  15. G

    Differential equation problem

    The last example on my homework assignment this week is this: Solve the following differential equation. y'' + 2y' + y = e^{-x} I started by solving it like it was y'' + 2y' +y = 0 (Instert y = e^ax and so on) and got the following equation and solution: e^{ax}(a^2 + 2a + 1) = 0 => a...
  16. G

    Integration problem - Please help

    Nope, I missed it. :rolleyes:
  17. G

    Integration problem - Please help

    Hmm... I did it by hand (subsitution, t = g + 1/2 kA/m v^2) and got this: y = -\frac{m}{kA}ln(1 + \frac{kAD}{m}) Which is the same as mathematica returned, but with an extra minus sign. Is it an error on my behalf?
  18. G

    E / natural logs

    True, but e^(pi * i) = -1. Doesn't that count?
  19. G

    E / natural logs

    Couldn't we say that \frac{e^x-5e^{-x}}{4}=1 also has two solutions, but only one in {R}?
  20. G

    Arc Length formula

    Oh, I see. That's odd. Are you sure that in the text they didn't mean that the result from the arclength formula should be x^2/2 + lnx/4 before you put in the limits?
  21. G

    Arc Length formula

    I don't see the problem, I don't get an extra 1/2 at the end. I get the same result as you do finding the function but I don't have any problem inputing back into the equation. f(x) = x^2 - \frac{ln|x|}{4} \frac{df(x)}{dx} = x - \frac{1}{4x} \frac{df(x)}{dx}^2 = x^2 - \frac{1}{2} +...
  22. G

    Growth at Zero Gravity

    If I recall correctly from last year's biology plants don't know which way's up and which way's down. But the plant growth hormone (Axin or something like that) gathers at the bottom of the seed (pulled down by gravity) and that causes the plant to "know" which way's up. The plants roots then...
  23. G

    Sinx and i

    I'm sorry, I'm from Iceland and math is tought in icelandic, so I don't know all the english names for functions. I'll look over what NateG posted tomorrow (kind of late here at GMT), since I've run into trouble deriving it myself the least I can do is learn how to do it properly. Thanks guys.
  24. G

    Sinx and i

    L = \int_{a}^{b}\sqrt(1 + (f'(x))^2)dx Anyway, thanks guys. Too bad that doesn't apply, seems the damn teacher was right. :smile:
  25. G

    Sinx and i

    Isn't that the definition of the sinh function? I always thought sin was defined as a/c in a triangle with one 90° corner.
  26. G

    Sinx and i

    Quick question. sin(-x) = -sin(x) this can be seen as this example: sin(i^2x) = i^2sin(x) Does this then apply? sin(ix) = isin(x) ? I'm trying to derive a formula for the length of a simple parabola. Unfortunetly in my calculations I end up with Arcsin(i2x) along the way and it...
  27. G

    I'm sure this has been asked a million times but,

    One year. We were debating a similar question in my physics class a couple of weeks ago. The difference was we were thinking that if you had a rigid pole in the pole/barn paradox, you'd be both outside the barn and inside at the same time. We argued about it for a very, very long time until...
  28. G

    Downward acceleration greater than G concept

    Actually the objeect isn't falling faster than g. It's speed is increasing but g (the accelaration) stays the same. It's no problem to fall faster than g, for example if you throw yourself out of an airplane you will be accelarating at a constant 9.8 m/s^2, one g (If there was no air to provide...
  29. G

    Work done

    It's the same in both cases, I beleive. In the first, the work done equals F*(s_2 - s_1). In the second, the man can never be sure if he's moving towards the chair or the chair towards him if it/he is moving at a constant velocity, so it can be treated exacly like the first example. Work then...
  30. G

    First victim of moon base/Mars mission?

    I don't think so. It may be possible to build bigger telescopes on the moon, but the bigger they are the bigger the risk of being hit by meteors.
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