Ordinary differential equations

An ordinary differential equation is one with (ordinary) derivatives of functions of a single variable each—time, in many applications. These typically describe quantities in some sort of lumped-parameter way: mass as a “point particle,” a spring’s force as a function of time-varying displacement across it, a resistor’s current as a function of time-varying voltage across it. Given the simplicity of such models in comparison to the wildness of nature, it is quite surprising how well they work for a great many phenomena. For instance, electronics, rigid body mechanics, population dynamics, bulk fluid mechanics, and bulk heat transfer can be lumped-parameter modeled.

Three good texts on PDEs for further study are kreyszig2011, TODO.