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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...