/sci/ - Science & Math

Well there is jerk and jounce and so on

http://en.wikipedia.org/wiki/Jerk_%28physics%29
http://en.wikipedia.org/wiki/Jounce

but pure dF can also made sense of in a way, as others pointed out. Although F is conventionally not a form a priori. But e.g. in Euclidean space, you can easily find that corrosponding object.
http://en.wikipedia.org/wiki/Musical_isomorphism

>>4180461

>and I'm teaching some physicists this semester in basic mathematics

for people in which semester?

And how in dept do you want to go? mention stuff, explain stuff, how many minutes/hours do you want to spent on topics?

http://www.youtube.com/watch?v=-Ht4qiDRZE8&feature=g-u

mind fucking blown

>>4104678
1) Yes, there are infinite such functions over R, namely all function, whos graph is symmetric with respect to the 45° axis (i.e. the function y(x)=x).
In more generality, see
http://en.wikipedia.org/wiki/Involution_%28mathematics%29
2) Yes, there are infinite such functions over R, namely the multiples of e^x.

>>4050297
Well, can you prove this?
The fact that is symmetric is, at least to me, not an evident argument for your statement. You start by applying a big force (which falls off after some time) and then you pull back by starting out with a small force.

It's more or less exactly the point I made above:
You want T+V=const. for the whole time and you argue that the work part W(V,d) must equal out the kinetic energy, which clearly goes from T(x=0)=0 to T(x=6)=0. But since you start out on a point with non-vanishing potential (big force at the beginning) the argument isn't so clear.

I actually gave a presentation 3 weeks ago, why the OPERA results violate special relativity and why it will turn out to be a measurement failure. I'm looking forward to see what happens now :D
In reality, I'm a big fan or starting from scrath with new ideas.

http://terrytao.wordpress.com/

Mostly stuff like harmonic analysis. But number theory too. He got the fields medal for a result in number theory after all!

Are you majoring in an applied science and you have to learn this kind of stuff for some weird reason or are you actually a theoretical physicist doing statistics (on 4chan?!)

http://en.wikipedia.org/wiki/Non-standard_calculus
http://en.wikipedia.org/wiki/Non-Standard_Analysis

Solving ODEs (all the different methody you leard to solve them) can be understood as search for good coordinates using Lie Group Analysis.
http://en.wikipedia.org/wiki/Lie_group

For two different t_i, you have two different operators H(t_i). They will not commute in general, but without the explicit construction you will have problems computing anything. If both t_i are the same, they trivially commute. If not, then usually you'll see to what extend they don't commute if you write down H in terms of creation and annihilation operators resp. quantum fields. Then, causally related field will never commute and therefore H won't too.

related:
http://en.wikipedia.org/wiki/Perturbation_theory_%28quantum_mechanics%29#Method_of_Dyson_series

okay OP, here is your matrix B construction procedure, dim n:

- choose A_{ij} with i<j, i not 1 freely
- A_{ij}=-A_{ji} for i>j
- A_{1j}=-(sum_{k1=2}^j A_{k1 j}+sum_{k2=j}^n A_{j k2})

such a matrix has ((n^2-n)/2)-(n-1) matrix entry degrees of freedom.

n |
1 | 0
2 | 0
3 | 1
4 | 3
5 | 6
6 | 10
7 | 15
8 | 21
9 | 28
10 | 36
11 | 45
12 | 55
13 | 66
14 | 78
15 | 91

I gave the example with n=3 above.

>>3615468
The quantum vacuum (or rather the empty equilibrium state) is not invariant under accelerations, which you experience when not trying to fall (into the black hole). Therefore an otherwise empty state (cyclic vector) appears excited = particle creation.
Writing down a Hamiltonian (time evolution) on a non-flat manifold and/or computing the propagator is a mess. Not having translation invariance (and therefore no obvious energy concept) is one of the main problems of quantum gravity in the classical QFT approach.