Recent content by tomelwood

Oh of course. Thanks. OK. So now all that section makes sense, the final step is to show that the trace terms cancel out. I've been trying to find out the intermediate steps going on, and have managed to solve the equation if I can show that...

Hi A topic came up in a lecture the other day about how if certain simplifications are made, then the Einstein equation reduces to a form of the wave equation. When I look at derivations of how this happens, I get a little confused as to how this happens. I think I'm posting it in the...

After further investigation, I have since discovered that these are just a fairly obscure way of writing tangential and radial accelerations. However, tangential acceleration is given by Equation 286 on this page http://farside.ph.utexas.edu/teaching/301/lectures/node89.html which upon...

Homework Statement I am reposting an edited version of this problem from a previous post of mine, due to it not being entirely relevant to that post, and also the question was asked after the thread had been replied to, so looks like an answered question. I also aim to give more detail here...

So rather than calculating the solar constant from the sun's power, rather the power of the sun is calculated from the observed solar constant. OK. I have since discovered that I can relate the power of the sun to the intensity of the sunlight passing through a sphere of radius r, simply by...

Homework Statement I am try to understand how the value of 1370 watts per metre squared for the intensity of sunlight hitting the Earth has been derived. Is there a way to see this mathematically? Homework Equations I understand about how the intensity is related to Poyntings vector, by...

Having investigated further, I have found that multiplying (1,1,0) by that quaternion that I didn't like does actually give (0,1,1) , but I don't understand how I can interpret that geometrically - ie about what axis and by what angle is the rotation being performed? Because the usual way of...

Homework Statement Hi, I am having problems in showing that in practise the composition of two rotations represented by quaternions is still a rotation. The example I have constructed is: Rotate (1,1,0) by 45 degrees about the z axis. The quaternion to use is thus q = cos(22.5)+ksin(22.5)...

Homework Statement Hello, I'm trying to get my head around the various properties of quaternions that all seem very similar, but I can't quite understand the underlying differences between them. I would like to know the differences between unit quaternions, purely imaginary quaternions...

Homework Statement I have to calculate the following line integral \int_{\gamma}y^{2}cos(xy^{2})dx + 2xycos(xy^{2})dy where \gamma is the path defined by the equations x(t) = t^{4} and y(t)=sin^{3}(\frac{t\pi}{2}) t between 0 and 1Homework Equations Now I know that the formula for calculating...

Homework Statement I am getting quite confused as to the concepts behind this task. I have a function given as a double integral, and am asked to find the gradient of it. However, I have no notes on how to do this, so it is either a very simple task, or the lecturer has once again missed...

Homework Statement Hey, just wondering how I might go about doing this problem, as I really have very little idea... Prove the following inequality: \frac{1}{e}\leq\frac{1}{4\pi^{2}}\int_{R}e^{cos(x-y)}dxdy\leqe (hopefully this reads "one over e is less than or equal to one over four pi...

If this is all true, then the covariance is now E[(X-2)(Y-1.5)]. How on Earth do you work that out??

If I am right in saying that to find f(x) and f(y) just integrate over the range of where it is defined, with respect to the other variable. Ie. f(x) = (integral between 1 and 0) of 6x dy = 6x and f(y) = (integral between 1 and 0) of 6x dx = 3 Now to find E[X] I do = (integral between 0 and 1)...

OK Having thought about it some more I have figured out the following: i) since the pdf (I realize that f is the pdf, and F is the cdf, not as I wrote before) is only defined for x on [0,1] and y on [0,1] and that for the definition of pdf I need to integrate everywhere they are defined and...