Recent content by saxen

1. Existence of solution legendre equation

Some corrections to my current solution
2. 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...

4. 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...
5. 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)
6. 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.
7. 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...
8. Distance between point and set

Thank you! I got it right.
9. 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.
10. 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...
11. 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.
12. 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?
13. 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...
14. 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.
15. Fourier transform

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