Recent content by dhris

You are most of the way there, you just need to plug your proposed solution into the boundary condition. First of all, since we're dealing with the unit disk, the normal direction is r, so n=r. Secondly, you'll want to rid yourself of the pesky u_c in the boundary condition. You can either make...

I think that's a little strong since not every linear partial differential equation is separable.

What's the problem? All you have done is multiply the normal derivative by f. There's no differential operation on f at all so you do not need to be concerned that it is a function rather than a scalar.

The x=pi/2 was just an example. It seems like the question even gives you the value of x you should use, so just plug it into the series and the function and you have your answer.

Usually the idea is to find some value of x that makes your Fourier series into the series in n that you want. If you choose x=pi/2 for example, cos(nx) will vanish for odd n. Then you'd plug your choice of x into the function f(x), for which you presumably have a closed form (but you haven't...

Yes, poor wording on my part. It may not make any difference to the calculation, but it's a huge difference if you happen to be Prisoner A!

Take P(J3|C2). This means that C2 will be executed. Therefore, the jailor has to free number 3 because there's no other choice - he's not going to free prisoner A in this scheme. So P(J3|C2)=1. The same applies to the next one. As for the last one, it's prisoner A to be executed, so each of the...

I would say that a general "Fourier expansion" is actually an integral. What (1) implies is that the modes are discrete and thus the integral becomes a sum, and therefore \omega=2 \pi/T , as Halls mentioned. Maybe this is the missing step you mean?

Oh man. I must have meant to say "some", and it came out as "any".

Yes, that seems to be the correct way to state it: http://en.wikipedia.org/wiki/Fundamental_lemma_of_calculus_of_variations It's for every function g not any function g.

This calculation will show you that the pressure on this face is different from that on the others. This can easily be seen from the tensor calculation, which is the correct way to do it. Nobody is disputing that measurements made in the rest frame don't change (post-acceleration that is)...

It has been explained about 4 times in this thread already. If you go back and read it you can see where 1effect was finally convinced that your calculation did not predict that the pressure is invariant. For god's sake, he even made a post addressing the explanation to you directly.

I hope he's not convinced of it, because it's not true.

What's the application? There are many numerical routines out there for doing various kinds of conformal maps. For example, the sctoolbox for Matlab, http://www.math.udel.edu/~driscoll/SC/ handles mappings to polygonal regions. And Zipper is a nice fast fortran program for conformal maps...

Ha, you beat me to it. Can you believe it took me at least 6 minutes to write my two-line post? Sure, but what does that get you?