## Saturday, September 5, 2009

### Derivations

Two years over and done with, and I have a good feeling for reading equations. This isn't always the case -- I'm still unpacking things as complex as, say, the Schrodinger equation, but give me something along the lines of chemical kinetics, a classical mechanics problem, or the ideal gas law: Yeah, I feel pretty good about reading the relationship. Just as I feel comfortable with reading equations, this year has a new angle being thrown at me: Deriving equations from other equations.

Holy shit, derivations are difficult. So far, I have no real "feel" for where to begin in deriving. I just write down two or three related equations, isolate some variables, do some substitutions, and play with the rules of logarithms hoping that all my random math play will, in the end, give me the equation that I'm looking for. To say the least, this doesn't help. I've been walked through deriving the ideal gas law using classical mechanics, and the derivation itself makes complete sense. But now, left on my own, I feel entirely stuck.

The current problem: Derive P^gamma V = constant from PT^f/2 = constant, where gamma = f+2/2, and f is the degrees of freedom. So, I have both forms of the ideal gas law, the first law of thermodynamics, a definition for work, and the equipartition theorem of energy... I think I could google something up, but this wouldn't help me in knowing how to actually derive equations, rather than follow arguments.

If you have any kind of method for deriving equations, then this is my desperate cry for help. In the end, I'll get it. But it'd be nice to see what other people do if and when they derive equations.

EDIT: In solving, I found a new "method" for derivations. Working backwards. By playing with the "end" result in the same way that I played with the beginning result, I was able to see a familiar form that I knew I could convert the beginning result to. Other than that... no method, really. More intuition.