Recent content by hanson

Thank you very much!

Anyone how to evaluate this integral? \int_{-1}^{1} (1-x^2) P_{n}^{'} P_m^{'} dx , where the primes represent derivative with respect to x ? I tried using different recurrence relations for derivatives of the Legendre polynomial, but it didn't get me anywhere...

Hi all, I am so confused by the famous Archimedes's story of telling if the crown is made of pure gold. As far as I understand from information posted in the internet, such as http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html Archimedes first determines the volume of the crown by...

Thanks lurflurf. Let me read it in detail.

Let's focus on the Laplace equation. Is there a good way to understand the following? If I have a fundamental solution f to the Laplace equation, then the gradient of f is also a solution to the Laplace equation. I can see why if I express Laplace equation in Cartesian coordinates, and see they...

Thank you very much!

Thanks for your reply. I think I get it, but why D[D^2+3D-7]=[D^3+3D^2-7D], but D[xD-1]=xD^2+D ? Should D[xD-1]=xD^2+D-D = xD^2?

Hello, if I have a fundamental solution, ,f, to a partial differential equation L(f)=0, where L is the differential operator, is that true that the derivatives of the fundamental solution, like D(f), will also be solution to the partial differential equation? Intuitively, is it because things...

A friend of mine spotted a calculation mistake... Somehow I read \Gamma^l_{ki} as \Gamma^l_{kj}... and \Gamma^l_{kj} as \Gamma^l_{ki}. I don't know why I didn't make this mistake for the previous terms but only for this term, and couldn't spot it...stupid mistake. Anyway, thank you for your help.

And I have using this page from wikipedia http://en.wikipedia.org/wiki/Curvilinear_coordinates

How about if S is the stress tensor, and I would like to find the gradient of the stress tensor, which is a third order tensor in cylindrical coordinates? I am calculating according to the definition of the gradient of a tensor given up, which is the same definition wikipedia used... I am not...

Hi all, I have been struggling (really) with this and hope someone can help me out. I would just like to compute the gradient of a tensor in cylindrical coordinates. I thought I got the right way to calculate and successfully computed several terms and check against the results given by...

Thanks arildno!

Oh...the "f' here refers to a general function? So, you get this formula basically by performing similar steps below, right? I have done this is the most boring and lengthy way In spherical coordinates, \nabla = \vec{i}_r \frac{\partial}{\partial r}+ \vec{i}_{\phi} \frac{1}{r}...

Hi, arildno. Thanks for the detail reply. But what if it is not a dot product between \nabla and \nabla \frac{1}{r}? If it is a dot product, then we will get a Laplacian. However, if it is like a "dyadic product" (I am not sure if this is the right term to use, but seems to be), then we should...