Thx for the suggestions, especially for Munich. But how about the other part of my question - is it worth it? I mean, leaving for a master's. Surely for PhD, but I do have doubts regarding master's.
Hi everyone!
I'm now doing my 3rd year of bachelor's study in physics at Jagiellonian Uni., Cracow, Poland. As good the university at the national scale as it is, I'm considering going for my master's degree somewhere abroad. Now, the pros are pretty obvious - almoste every European university...
Wrong order of convergence while using method of lines
Hi!
Still fighting with radial wave equation :/. I've split it into 2 first order equations in time and am using method of lines to integrate it with RK4 as my time integrator, which is O(h^4). My spatial derivatives are are approximated...
Homework Statement
Well, I'm not sure if this is a correct subforum to post my problem, but to me it does seem to me as an academic problem. One I can not solve, apparently.
Well, anyway. I'm solving the 1+1 radial wave equation using finite difference. I shifted my grid, so that the origin...
Hello everyone and greetings from my internship!
It's weekend and I'm struggling with my numerical solution of a 1+1 wave equation.
Now, since I'm eventually going to simulate a black hole ( :D ) I need a one-side open grid - using advection equation as my boundary condition on the end of my...
Homework Statement
Assuming that transformation q->f(q,t) is a symmetry of a lagrangian show that the quantity
f\frac{\partial L}{\partial q'} is a constant of motion (q'=\frac{dq}{dt}).
2. Noether's theorem
http://en.wikipedia.org/wiki/Noether's_theorem
The Attempt at a Solution...
What I was recently taught is:
-4 \pi i \int\limits_0^{\infty} log(x) R(x) + 4 \pi^2 \int\limits_0^{\infty} R(x) = 2 \pi i \sum res ( log^2 (z) R(z) )
R(x) being rational function with no poles for x>0 and such that lim x*R(x)=0 when x->infinity. That should work for your function. And since...
Yep, but your car ain't going to fly :P. I mean, increasing velocity increases force neaded for a car to turn and it works only in XY plane. Fn is constant all the time.
Right side is a determinant of this matrix. It's not so hard to prove, you could in example use Levi-Civita symbol to write your cross product, it goes in 3 steps afterwards.
Why would your frictional force be equal to Fn-mg? your friction force is lesser than or equal to \mu F_n , \mu being friction coefficient. In our case we want our friction force to be as big as it can, hence F_f = \mu F_n .
Whoa, whoa, whoa, wait ;). The left-sided limit definitely doesn't exist, since in Reals there is no logarithm of negative number. But why would the right-sided limit not exist? I mean, infinity is a kind of a limit, isn't it?
Imagine your car taking a turn. It can, as long as force of the friction serves as a centripetal force (this is indeed the force that makes your car turn ;)). Hence they both have to be equal. Now, the force of the friction is the force that the car applies to the surface of the road multiplied...
Well, since anti-derivative of \frac{1}{x} is Log|x|, we eventually get lim_{\epsilon -> 0} Log|-\epsilon| - lim_{\delta -> 0} Log|delta| , which again is \infty - \infty . Basically, I can't see much difference between those 2 limits you wrote (one with epsilon and delta and one for...
Homework Statement
I'd like to prove the inexistence of \int_{-1}^1 \frac{1}{x} dx , or at least that it's not 0.
Homework Equations
Well... :P
The Attempt at a Solution
Since integrating is linear, we can write \int_{-1}^1 \frac{1}{x} dx = \int_{-1}^0 \frac{dx}{x} + \int_0^1...