# Search results

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.
16. ### Fourier transform

Sorry, but I don't understand what you mean. Do you mean how I technically evaluate it?
17. ### Fourier transform

Homework Statement Hi y'all, ran into some trouble with a fourier transform Im supposed to find the fourier transform of f(x)=\frac{1}{x^{2}+6x+13} Homework Equations Not that I know The Attempt at a Solution I tried integrating this with no luck. All help is as usual...
18. ### Minimizing a integral

Sorry but I don't really get it. We seem to be thinking the same, rewriting with orthonormal basis, but after that?
19. ### Why do people drink?

Because beer tastes great and being drunk is fun!
20. ### I am in need of help ( Idiot here)

Don't call yourself a idiot just becuase you are stuck. You go to school to learn right? You can't know everything up front!
21. ### Minimizing a integral

Sorry! Missed that the integral is between 0 and 1
22. ### Minimizing a integral

Homework Statement Determine the polynomial of the form P(x)=x^3+ax^2+bx+c that minimizes \int[P(x)]^2 Homework Equations The Attempt at a Solution My first thought was that I should find a second degree polynomial that minimizes x^3. That didn't work at all! So now I'm...
23. ### Problem concerning square roots

"x+ square(5x + 10) - 8 = 0" is it square root or x+(5x+10)^2-8=0 ?
24. ### PDE: heat equation

I tried this problem again this morning and solved after 5 minutes. I am sooooo stupid. sinx*cos4x = 1/2*(sin3x+sin5x) So: ∑Bn∗sinnx = 1/2(sin3x+sin5x) ---> Bn1sinn1x+Bn2+sinn2=1/2(sin3x+sin5x) Bn1=Bn2=1/2 n1=3 n2=5 And its solved. That is all.
25. ### How do you cope when failing a math test =/?

When I failed my first exam I got roaring drunk, but I wouldn't recommend it. Didn't help me at all... One exam dosen't really matter, just pass the next one.
26. ### PDE: heat equation

Thanks! Pat on back is well deserved =). Will try this. Do you think there is a way to solve this analytical?
27. ### PDE: heat equation

Thanks dude, this problem is driving me insane.
28. ### Need some help with an integral.

This integral is solvable with integration by parts. Notice that you started with x^3 and after your first integration you have x^2. So just keep integrating!
29. ### PDE: heat equation

Bn= 2/L *integral sinx*cos4x*sinnpix/L L should be pi since my intervall is 0 to pi, or have I misunderstood something? Then integral becomes: http://www.wolframalpha.com/input/?i=integrate+sinx*cos4x*sin%28n*x%29 sin(n+5)pi should be zero for all n?
30. ### PDE: heat equation

Homework Statement u_{t}=3u_{xx} x=[0,pi] u(0,t)=u(pi,t)=0 u(x,0)=sinx*cos4x Homework Equations The Attempt at a Solution with separation of variables and boundry conditions I get: u(x,t)= \sumB_{n}e^-3n^{2)}}*sinnx u(x,0)=sinx*cos4x f(x)=sinx*cos4x=\sumB_{n}*sinnx...