Recent content by saxen

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    Existence of solution legendre equation

    Some corrections to my current solution
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    Show that limit set of dynamical system is closed

    I forgot about this thread. I had some problem with the last part of this question but found a proof that helped me: phi denotes the flow. Let y be in the closure of w(x). Then there exists a sequence y_n in w(x) such that |y-y_n| < 1/2n. Moreover chosoe a sequence s.t t_n --> inf |phi...
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    Transition matrix and rational canonical form

    Hi! edit: sorry, I misread
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    Existence of solution legendre equation

    Hi all, I have my exam in differential equations in one week so I will probably post alot of question. I hope you wont get tired of me! Homework Statement This is Legendres differential equation of order n. Determine an interval [0 t_0] such that the basic existence theorem guarantees a...
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    Find the solution?

    Divide both sides with (s^2+3s+2) Y(s)=1/(s^2+2s+3)(s^2+1)+e^(-3pi*s)/(s^2+2s+3)
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    Find the solution?

    Divide with (s^2+3s+2) then you might have to do a partial fraction decomposition so you can find the inverse.
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    Show that limit set of dynamical system is closed

    Homework Statement Define the w-limit set (omega) of a point. Show that w(x) is closed. Homework Equations The Attempt at a Solution The definition of a limit set is the set of points to which there exists a sequence t_n→∞ such that \phi(t_n,x) → y The second question. I was...
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    Distance between point and set

    Thank you! I got it right.
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    Distance between point and set

    Ah yes! I actually tried the triangle inequality but failed. I am going to try again! Could you please elaborate some more on the second part? I have been stuck on similar questions because I do not understand this argument.
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    Distance between point and set

    \inHomework Statement Denote by d(x,A) = inf |x-y|,y \in A, the distance between a point x \in R^n and a set A \subseteq R^n. Show |d(x,A)-d(z,A)| \leq |x-z| In particular, x → d(x,A) is continuous Homework Equations The Attempt at a Solution I have no idea on how to prove this. I drew...
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    Hard fourier transform

    Ah, I was thinking right at least. Its so stupid, we don't get any of these rules on our exam so without wiki, I would have never solved this exercise. Thanks for the help.
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    Hard fourier transform

    Hello sussking_leon, My bad, the * means multiplication and not convolution. How do you get the i \xi infront of the exponent?
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    Hard fourier transform

    Homework Statement Using that the Fourier transform of e^{|x|} is \frac{2}{\xi^2+1}. Compute the Fourier transform of \frac{x}{(x^2+1)^2} Homework Equations The Attempt at a Solution My first thought was to try and rewrite the problem in a form I recognized, tried a couple of things but...
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    Matlab - Numerical Analysis

    If you look in the first row of the for loop, the vector v is not defined so the code dosen't make sense.
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    Fourier transform

    Well then, not much else to then lock thread I guess. Will call a friend instead. Thank you for reading though.
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