Just want to clarify something more rigorously for you mathematically inclined folks:
We were talking about how to calculate Omega_total for the case in which one system exchanges energy with another. We wrote the following down:
Omega_total = Sum Omega_1(E1 - dE) Omega_2(E2 + dE)
What we were saying in class was that Omega_total is strongly peaked around its maximum value. By strongly peaked, what we mean specifically is that we can approximate the above equation just using the maximum term, rather than the complete sum:
Omega_total = Omega_1(E1 - dE*) Omega_2(E2 + dE*)
where dE* is the value of dE that maximizes this equation. This is actually called the "maximum term method."
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