Recent content by Gunni

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    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...
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    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.
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    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?
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    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.
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    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...
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    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...
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    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...
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    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?
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    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.
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    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.
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    Differential equation problem

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