Press Schechter function -- the variance on mass scale

[classy cal]

In obtaining the Press Schechter function, the variance on mass scale is differentiated with respect to mass. The variance on a mass scale is a function of wavenumber k through the Power spectrum and transfer function. To eliminate k dependence, some value of k must be inserted into the variance on mass scale. Can someone explain how this is done?

 

[kimbyd]

I believe they're assuming linear theory, such that each wavenumber $k$ is independent. This allows us to treat functions of $k$ as simple variables. Perhaps these notes will help:
http://w.astro.berkeley.edu/~mwhite/teachdir/mini_ps.pdf

Edit:
Here's another source, that takes a bit more time to explain the details of the derivation:
http://www.aip.de/summerschool2006/lectures/eps.pdf