Hi there I've heard from various applied mathematicians that the D.E. that models harmonic motion is one of the most important in physics...apparently it appears in nearly every conceivable field, from quantum mechanics to cosmology (something to do with modelling the cosmic microwave background)? Accordingly I've decided that it might be beneficial if I tried to read widely on harmonic oscillators. I'm a first-year physics/appl. maths major. I've covered Feynman's treatment of the topic (Lectures Vol. I chapters 21-24 I think) and other than that I've encountered it, though on a basic level, in my introductory mechanics and statistical mechanics courses. Is the harmonic oscillator really as important as I've heard? And if so, could you recommend with which topics I might start and how I could proceed? Also, if I could use this as a platform to get to grips with some new math (or at least, math I would encounter only later in my studies) then that would be a bonus... Thanks in advance!