Recent content by SqueeSpleen

Homework Statement We have an inclined plane with a mass ##M## and an angle ##\alpha## and a box of mass ##m## over it. Everything is at the instant 0 (it's a problem of static, no dynamics). a) What's the acceleration in the component x of the box? b) What's the acceleration in the component y...

My university library has almost no math books (I think it has 3 different books on differential equations and 1 on metric topology and that's the most advanced thing it has), but where I live there's an institute where they have engineering and physics undergrad and graduate students, it has a...

Sorry, I probably should have waited after reading Sturm - Liouville theory before approaching these exercises. I only had done exercises without reaching that chapter, but today I will read about this to be able to solve the problems in a more systematic way instead of having to try in this way.

Oh I think that I got it. I should use a series of cosines like ## \cos ( (n+ \dfrac{1}{2} ) \dfrac{ \pi }{L} x ) ## In which case, it's the same as the series I used. I'm not sure how to do a reasoning to arrive this cosine series, but perhaps doubling the interval so I'm changing ## \dfrac{...

I may be understanding something bad, but: $$ \int_{0}^{\pi} \cos (nx) dx = \dfrac{1}{n} \sin (nx) \bigg|_{0}^{\pi} = 0, \qquad \forall n \in \mathbb{N} $$ I checked with calculator to see if I was making a mistake integrating and I still have this equal to zero, at least for n=1,2,3 and 4, but...

First of all, sorry for the poor redaction. I have re-read what I wrote and when I meant "as the zero eigenvalue is discarded" I wrote "as the constant eigenvalue is discarded" which makes no sense at all. Yes, that's why I said that I have solution only for the constant equal to zero, I...

Homework Statement I have to solve the following problem $$ \left\{ \begin{array}{ll} \dfrac{ \partial^{2} u }{ \partial x^{2} } + \dfrac{ \partial^{2} u }{ \partial y^{2} } =0 & \qquad \forall x \in (0, L), y > 0 \\ & \\ \dfrac{ \partial u }{ \partial x } (0,y) =0, & \qquad \forall y > 0 \\ &...

Oh. I'm self studying PDE, I have been given a book to follow but it has too few topics. A good book to learn about green's functions? Is Evan's one recommended? Laplace transform was very good, even for the case ##a= \omega ##

Oh thank you! I didn't use the Laplace transform since I finish my ODE course. This is going to be fun :D

Working a little more I've got $$ y(t) = \frac{1}{2} \dfrac{ b }{ \omega^{2} - a^{2} } \bigg( a \sin ( ( \omega+a) x ) \sin (x \omega) + \omega \sin ( (\omega-a) x ) \cos (x \omega) \bigg) + c \sin (x \omega ) $$ I probably made a mistake in a previous step.

Homework Statement I was reading a PDE book with a problem of resonance $$ y_{tt} (x,t) = y_{xx} (x,t) + A \sin( \omega t) $$ After some work it arrived to a problem of variation of parameters for each odd eigenvalue. To solve it, it uses $$ y''(t)+a^{2} y(t) = b \sin ( \omega t) \qquad y(0)=0...

Yes, I may have phrases it wrongly. I will have to study Sturm Liouville Theorem. I know about basis from functional analysis course, what I tried to ask is why they failed to be a complete orthonormal set.

Oh, thank you very much. I supposed they could do it but wasn't really sure. They are not dense of they're only not orthonormal? I will check that myself.

I've solving some separation of variables exercises, and I have a doubt when it comes to the Laplacian $$ u_{xx} +u_{yy} =0 $$ I usually have a rectangle as boundary conditions, so I use the principe of superposition and arrive to $$ \dfrac{X''(x)}{X(x)} = - \dfrac{Y''(y)}{Y(y)} = - \lambda $$...

Yeah, but I was trying to let this elementary. As they hadn't studied DE formally in this course, I didn't want to mention that's a DE. But in the end what I'm doing is variation of parameters... But yeah, your solution and huntman's one are way more straightforward, and even if I wanted to keep...