This was one of those annoying papers where, for the most part, you learn a bunch of formulae without a proof and when you’re given the proof it’s all funny. Boring, but easy since you don’t have to do much work. However, sometimes you just need all the formulae, you need a cheat sheet, because the exam is tomorrow. Unfortunately, I couldn’t manage that, so a lot searching, a little deriving, and some searching for old books allowed me to type them all up and print them up. Might as well save some other soul some trouble. Go to Mathworld for the proofs. You could also wander around the Springer Encyclopaedia of Mathematics or PlanetMath.
Most of the stuff is particular to the course we’re doing, so some things are assumed. For example, the Runge-Kutta method refers to the Fourth Order Runge-Kutta method and stuff like that. Also, parts may be technically inaccurate or may be plain unhelpful :) , but that’s because that part will just jog the right part of my mind. Sorry.