OK, thanks for the help.
But I still don't understand why we can't replace N with N=\sum_{i=1}^n N_i in the equation before we do the partial differentiation.
Note the first equation could be written
f(N_1,...N_n)=N\ln(N)-N + \alpha N + \beta E + N \sum_{i=1}^n (N_i \ln(g_i) - N_i \ln...
I have a question about the Lagrange Multiplier method used to derive the Boltzmann distribution. I'm following the first http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics" .
I can get to this equation fine:
And I understand how they get the next line...
I'm 2nd year math phys under science, and I think the programs are identical after first year. There are a lot of crosslisted courses under AMATH and PHYS, so it may look like math based students take more, but its really the same. The main difference up until now was Quantum 2 - math students...