**Derivations**

Often times, I run into an equation that I don't know how to derive. Naturally, I spend time trying to derive it myself, or finding some other resource that explains the derivation. But sometimes, the resources I find aren't satisfactory for one reason or another: too narrow in scope, too hand-wavy, too bogged down in mathematical rigor, or too broad to be easily applicable. Basically, if I can't find a resource that provides a derivation satisfying my own personal taste, I'll put it up on here. If you find any mistakes, please send them to me (see the contact form in the about section).

**Stirling's Approximation**

In this derivation, I seek out the derivation for Stirling's approximation for large factorials, using principles from asymptotic analysis, and furthermore, I try and expand the derivation beyond the usual first or second orders typically provided.

**Fourier Inversion Theorem**

In this derivation, I try to figure out where the factor of $2\pi$ comes from in the inverse Fourier transform. Turns out (at least doing it my way), it's a lot harder than it seems.