Here's my attempt, I hope it helps. I find reading this stuff is always pretty cryptic:
Let a=b therefore exists 1xa,1ya such that a*1xa=a, 1ya*a=a
Let b=1xa therefore exists -xa such that a*-xa=1xa
Let b=1ya therefore exists -ya such that -ya*a=1ya
Therefore...
My thoughts so far go along the lines of (but I don't really know what I'm talking about):
f(a)=f(b) so at least one f'(c)=0 on the closed interval [a,b].
But also f'(a)=f'(b)=0 so we have at least 3 turning points in f'(x) in (a,b).
Therefore need at least 2 turning points in f''(x) in (a,b)...
Homework Statement
Solve for y: (note the one in the title is wrong)
\frac{d^2y}{dx^2} = -2xy \frac{dy}{dx}
Homework Equations
None that I can think of.
The Attempt at a Solution
Oh so many failures. None which solved anything. I don't even know if this equation is solvable. :(
Well I...
Hi,
Is there a difference between
\int f(x,y(x)) dx
And
\int f(x,y(x)) \partial x
?
If so, how is the total integral written in terms of partial integrals?
Thanks for your help.
Hi,
I have been going round in circles trying to figure it out so I figured it would be quickest and easiest to just ask:
What is the definition of: \int f(x) d^4 x
I first thought it was:
=\int \int \int \int f(x) dx^1 dx^2 dx^3 dx^4
but now I am starting to think it is...
This calculation is only for a object moving in circular motion.
If an object is moving at a constant speed then it goes in a straight line. If however it keeps changing direction then it must be accelerating in the new direction. An object moving in a circular direction, as in the video you...
Well it seems that these smaller (angle, and hence size) peaks are the harmonics of the big (sound horizon size) oscillations. And their smaller temperature fluctuations is due to diffusion at recombination that thermalized a little which effected the smaller sized peaks more than the bigger.
My google searches for answers took me back to my post! That can't be a good sign.
Thinking further I'm staring to think I'm wrong saying:
These don't make sense. I doesn't matter what size the particle horizon is SINCE last scattering. It matters what the particle horizon was AT last...
Nope sorry. Acoustic peaks are due to gravitation vs photon pressure causing plasma oscillations in the early universe (when it was all plasma). Then last scattering happened, so no more plasma to oscillate and and we see the evidence as fluctuations in the CMB (radiation shocks from the...
I am supposed to have a qualitive knowledge of acoustic peaks for my exam, so none of the maths. After reading around I am still left with a few questions.
Is the first acoustic peak from the acoustic oscillations at last scattering? I imagine there were many oscillations before then but we...
In my textbooks every now and again it says "these equations can't be solved analytically" or just "this can't be solved". For example my current book claims:
\frac{dx}{dt}=-kBe^{kz}\sin(kx-\omega t) , and
\frac{dz}{dt}=kBe^{kz}\cos(kx-\omega t) ,
can't be solved analytically.
How...