Recent content by Uan

Thanks, that clears a lot up. So really the Lambert W in this case doesn't help all that much - just allows the function to be in a more recognisable form. You still need to go back to... \frac{1}{d}e^{\frac{b}{c}} = xe^{\frac{ax}{c}} and solve numerically for x.

Not really sure where this question belongs in this forum... I was solving an engineering problem and I got to the form ax=b-cln(dx) where a, b, c and d are constant real values. I had a peek at the answer and they got a unique positive real valued answer for x but I have no idea how...

Hi pwsnafu, I see what you mean about linear operators, but I have never used or seen the Dirac delta in that way. This is the first time I've heard about functionals, so I will probably will have to learn about them properly first before I fully understand how the Dirac delta is a...

Hi HallsofIvy, I was solving for the discrete Fourier transform of δ(n) and wondering why is was 1, but I didn't know until now that there are two generalized functions that share the same symbol δ, the continuous Dirac delta and the discrete Kronecker delta. Also for the Dirac delta, I...

What is the sum of an infinite Dirac series and why? 1 or infinity? \sum_{n=-\infty}^{\infty}\delta (n) I can see it being 1 because it's like a series version of the integral: \int_{-\infty}^{\infty}\delta (t)dt = 1 But for the series where n=0, \delta (0) = \infty :confused:

As luck would have it after posting, found the answer here: https://www.physicsforums.com/showthread.php?t=493424 Time for a rest... :zzz:

Hi, We can use Laplace transforms to solve DEs with these guys: But what are the z transform versions in discrete time that include initial conditions, and how do you derive them? For example y[n+1], y[n+2] etc. Thanks

Cheers jbunniii, just what I was after! :thumbs:

Hi vanhees71, I get the substitution but I don't see how they went from the integral to the next bit. To me, the form of the integral doesn't quite match the definition in my first post, it has got g(u) but the exponential has exp(-i*2*pi*f*(u/c)), so this is where I get hung up... Needs...

Hi, I'm following the proof of the "Scaling Property of the Fourier Transform" from here: http://www.thefouriertransform.com/transform/properties.php ...but don't understand how they went from the integral to the right hand term here: The definition of the Fourier Trasform they...

Ah yes! That works out beautifully! Cheers! :thumbs: [SIZE="1"](Formula 1 Qualifying at Spa! :wink:)

Ohh yeaahhh! Small angle approximation duh! Thanks tiny-tim! I really appreciate your help! By the way, I derived it as rsin(dθ), = rdθ, as when the angle dθ goes infinitely small in the triangle with sidelengths r, r and dθ (I've redrawn it), its like it has 2 right angles (180° ~= 90° + 90° +...

Ok that makes sense. One other question... How do they get the side lengths r*d(theta) and r*sin(theta)*d(phi) of element dA in the diagram below?

Hi, Started to learn about Jacobians recently and found something I do not understand. Say there is a vector field F(r, phi, theta), and I want to find the flux across the surface of a sphere. eg: ∫∫F⋅dA Do I need to use the Jacobian if the function is already in spherical...