z

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Ze Proof of Death



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Mon Feb 25, 2008 7:43 am
Snoink says...



Well... I think it's pretty. ^_^
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Ubi caritas est vera, Deus ibi est.

"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach

Moth and Myth <- My comic! :D
  





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Mon Feb 25, 2008 7:43 am
Snoink says...



Page 2! :D
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Ubi caritas est vera, Deus ibi est.

"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach

Moth and Myth <- My comic! :D
  





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Mon Feb 25, 2008 7:44 am
Snoink says...



Page 3! :D
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Ubi caritas est vera, Deus ibi est.

"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach

Moth and Myth <- My comic! :D
  





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Mon Feb 25, 2008 7:45 am
Snoink says...



Finally!
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Ubi caritas est vera, Deus ibi est.

"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach

Moth and Myth <- My comic! :D
  





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Mon Feb 25, 2008 7:48 am
Teague says...



*standing ovation*

It's amazing! Nobel Prize material right here!

Rofl. I dig your notes. They're like, eight degrees of awesome. The sidenotes are hysterical. xD

Yay maths gibberish that means absolutely nothing to me! =D

-Saint Razorblade
The Official YWS Pirate :pirate3:

P.S. Waiting for you to post this = I had to find something else to do = I can't go to bed until said thing is done. SO FEEL GUILTY.
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Mon Feb 25, 2008 7:51 am
Meshugenah says...



This makes me miss calculus. Then I look at it and remember why I hate math.

*applauds*

Yes, very pretty.
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Mon Feb 25, 2008 8:29 am
Incandescence says...



Snoinkus,

Code: Select all
I have a bit of difficulty regarding how you start.

Let P=f(e)--this is fine. Then (you claim):

P_0+P_e=f(p_0+p_e)

However, this is a bit of a mystery since, in general, f(x+y)≠f(x)+f(y) unless f is a homomorphism. In the interest of non-mathematical pursuit, I think you can safely get away with this kind of sleight of hand.

However! It is absolutely NOT true that

f(p_0+p_e)-f(p_e)
------------------  = f'(p_0)
        p_e

Indeed, this is only a true statement if you include the limit, i.e.

             f(p_0+p_e)-f(p_e)
  lim      ---------------------- = f'(p_0)
p_e-->0            p_e

I don't mean to be a spoil-sport; it's just a nontrivial amount of hand-waving to achieve your results. A less...suspicious way to do things might be something like the following:

Let u(x,t) represent a displacement of a particle in some direction of the point x at time t>0. Let U be an open set and V an smooth subregion of U. The acceleration within V is then

         /              /
d^2     |            |
----    | u dx =    | u_{tt} dx
dt^2  /             /
       V               V

where u_{tt} represents the second partial derivative of u with respect to t, and the net contact force is

   /
  |
- | F µ dS ,
  /
   ∂V

where F denotes the force acting on V through the boundary ∂V and the mass density is taken to be unity. Newton's law asserts the mass times the acceleration equals the net force, i.e.:

  /                   /
 |                   |
 | u_{tt} dx = - | F µ dS .
/                    /
 V                   ∂V

This identity holds for each subregion V and so

u_{tt} = - div(F).

Since we can safely assume air is an "elastic" body, F is a function of the displacement gradient Du; whence

u_{tt}+div(F(Du))=0

and for small Du, the linearization F(Du) ~ -aDu is often appropriate; and so

u_{tt} - a∆u = 0 .

This is the wave equation for propagation of sound when a, some arbitary constant, is given by a=c^2 and c is the speed of sound.


I have no idea why the integral signs are messed up so much. Silly non-TeX environments!

Cheers, and good to see some math around here!
Brad
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Mon Feb 25, 2008 6:26 pm
busboys and poets says...



o_O

O_o

I'll stick with my thesaurus, thank you. ^_^

Brava, though!
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