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...
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...
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...
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.
\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...
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.
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...
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...
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...
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.
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.
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!
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?
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...