Recent content by lesdes

Great! There is a follow up problem in my assignment to the one here (like check for uniform convergence, ##L^2##-convergence). I will first go and read my notes and book about that, especially ##L^2##-convergence since I have never done that. Then attempt so solve that problem. If I will have...

Yes thank you! I totally missed the parentheses there and I also noticed that I butchered the syntax of Mathematica. It should be Cos[] and not Cos(). Now I have the following plot for ##n=10## and ##n=100## for the Fourier series So my Fourier series is correct then, I suppose?

So I went over it again and I noticed the following error in ##a_0##. It should be ##a_0=\frac{1}{2}## and not ##a_0=2##. Also now I have the Fourier series for ##f## given by $$S_n(x) = \frac{1}{2} - \frac{2}{\pi}cosx + \frac{2}{3\pi}cos3x - \frac{2}{5\pi}cos5x + ... = \frac{1}{2} +...

Ah yes. I accidentally used the ##a_n## in the definition for the Fourier expression from post 1 as ##b_n##. I think I mixed them up. I will look at it tomorrow. It's 4 am now. Probably that is also the reason for such silly mistakes.

This is what I have done. ##a_0 = \frac{1}{2\pi}(\int_{-\pi}^{-\frac{\pi}{2}} 1 \, dx + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} 0 \, dx + \int_{\frac{\pi}{2}}^{\pi} 1 \, dx = \frac{1}{2\pi}(x\left. \right|_{-\pi}^{-\frac{\pi}{2}} + 0 + x\left. \right|_{\frac{\pi}{2}}^{\pi}) =...

Thank you. I will try and solve it and if I run into any more problems I will come back here or if I arrive at a solution. Well, the course is Linear Algebra and Fourier Series. The prof just said when he explained the topic of Fourier series "We will make a cut here (he referred to...

Homework Statement Find the Fourier series of the function ##f## given by ##f(x) = 1##, ##|x| \geq \frac{\pi}{2}## and ##f(x) = 0##, ##|x| \leq \frac{\pi}{2}## over the interval ##[-\pi, \pi]##. Homework Equations From my lecture notes, the Fourier series is ##f(t) = \frac{a_0}{2}*1 +...

So now I've plotted both equations in mathematica and I have the following results It might be that I did not understand the quadratic form purpose. I thought the purpose was to write a more complicated equation into a simpler form. I am a little bit confused now.

Ah yes now I see. I have the same result through mathematica. So now I have ##-7x^2 + 2y^2 = 5##. This result should be equivalent to ##−5x^2+y^2−z^2+4xy+6xz=5## as I understand it? Hence if I graph both in mathematica, then I should receive the same graph?

Yes there is a sign error in the eigenvalue matrix. But I only made the error when typing it in this thread. I will correct that now. You do not have to check whether the eigenvalues, eigenvectors and the multiplication ##P^TAP## is correct. I let Mathematica do the computations. But where do I...

Okay so let's see if I am on the right path. What I have done is that I have written ##−5x2+y2−z2+4xy+6xz=5## in the form $$ (x y z) \begin{pmatrix} -5 & 2 & 3 \\ 2 & 1 & 0 \\ 3 & 0 & -1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = 5 $$ as suggested by the book: is then . Next, I...

<Moderator's note: Moved from a technical forum and thus no template.> Hello I am given the following problem to solve. Identify the quadratic form given by ##-5x^2 + y^2 - z^2 + 4xy + 6xz = 5##. Finally, plot it. I cannot seem to understand what I have to do. The textbook chapter on...