Fork me on GitHub
Math for the people, by the people.

User login

Differential operator question

Primary tabs

Differential operator question

In working through a problem on the application of Christoffel symbolsPlanetmathPlanetmath, I came across an author’s answer to a problem

Γ

_αα^i = ∂∂x^α( ∂¯x^r∂x ) ∂x^i∂¯x^r = ( d_α  ∂¯x^r∂x )∂x^i∂¯x^r = d_α  δ_α^i

which confused me, since I have not see the a ”d” operator used before


I cannot ask this question without figuring out how to enter the LaTeX string. It is not displaying correctly in the original, which was posted before I was done.

The LaTeX equation appeared correclty when constructed at http://www.codecogs.com/latex/eqneditor.php. What am I doing wrong to have it appear correclty here?

My question is this. How does the author appear to take the last partial derivative into the parenthesis and effectively cancel the x, bar r terms and end up with the Kronecker delta result?

Thanks.

Here is an image of the equation I am trying to enter.

Not having much luck with this site.

I used to post an image, and that did not work, either.

My image is at http://planetmath.org/node/87495

Among other things, the fact that Ctrl-V does not paste things is annoying.

Is this site really this hard to use?

\includegraphics{Eq1.jpg}

Works for me.

These mechanisms will be streamlined eventually. Sorry for any frustration in the mean times.

$\Gamma _{\alpha \alpha }^{i} = ... = d_{\alpha }\, \delta _{\alpha }^{i}$

Γααi=xα(x¯rx)xix¯r=(dαx¯rx)xix¯r=dαδαisuperscriptsubscriptnormal-Γααisuperscriptxαsuperscriptnormal-¯xrxsuperscriptxisuperscriptnormal-¯xrsubscriptdαsuperscriptnormal-¯xrxsuperscriptxisuperscriptnormal-¯xrsubscriptdαsuperscriptsubscriptδαi\Gamma_{{\alpha\alpha}}^{{i}}=\frac{\partial}{\partial x^{{\alpha}}}\left(% \frac{\partial\bar{x}^{{r}}}{\partial x}\right)\frac{\partial x^{{i}}}{% \partial\bar{x}^{{r}}}=\left(d_{{\alpha}}\,\frac{\partial\bar{x}^{{r}}}{% \partial x}\right)\frac{\partial x^{{i}}}{\partial\bar{x}^{{r}}}=d_{{\alpha}}% \,\delta_{{\alpha}}^{{i}}

Subscribe to Comments for "Differential operator question"