Solving Diff EQs
Copyright 2005 by Jeff Suzuki
For some reason or another I looked up the lyrics to "Waltzing Matilda". Among other things I realized that 1) most people don't know the words to the song, 2) I didn't know the words to the song, and 3) some of the words weren't words.
In regards to the last point, I should say that they were words, just not standard English: they were Australian. Now that I've learned to speak 'strine, I know that billabong, coolibah, and the like really refer to objects and aren't just nonsense syllables.
This got me thinking: mathematics probably sounds a lot like Australian to non-mathematicians. Originally the refrain was "splining the functors", but it soon became apparent that mathematical terminology is hopelessly pedestrian: we use words like set, field, domain, smooth, and similar terms. In other words, the terms aren't outlandish, just their meanings (at least, to a non-mathematician).
In response I decided to write the following. Note that the third line of the chorus is always the third line of the preceding verse. This really wants a final verse (something about the "ghost of chaos" cropping up in loosely coupled systems), but I decided to leave this as an exercise for the reader...
Once a jolly math man hooked a mass upon a spring In SHM the whole thing set he
And he sang as he watched and waited 'til it settled down,
"You'll come a-solving diff-EQs with me..."
Chorus Solving diff-EQs, solving diff-EQs, You'll come a-solving diff-EQs with me, Third line of previous verse You'll come a-solving diff-EQs with me. "Frictionless motion, 'long a horizontal plane, Gives us a sine solution you'll see!" And he sang as he wrote down a second order ODE,
"You'll come a-solving diff-EQs with me."
Chorus Up came some damping to represent a friction loss. Down pulled the force of gravity, And he sang as changed the equations marching 'cross the board, "You'll come a-solving diff-EQs with me." Chorus "Let's add some forcing to make it look a real mess, But it can still be solved easily, For a linear operator makes the system homogeneous, You'll come a-solving diff-EQs with me." Chorus
Footnotes
SHM = simple harmonic motion.
Diff-EQs: Most of us pronounce this as "diff ee cues".
Namely x'' = -kx.