I wrote up a little primer on differential equations for neuroscientists. It can be found here: http://science.ethomson.net/Diff_Eq.pdf. Any comments or suggestions appreciated, especially at this early stage!
Here is the first paragraph:
Ordinary first-order differential equations come up frequently in neuroscience. They are used to model many fundamental processes such as passive membrane dynamics and gating kinetics in individual ion channels. When the equations come up, most electrophysiology texts provide the solution, but do not provide any explanation. This manuscript tries to fill the gap, providing an introduction to many of the mathematical facets of the first-order differential equation. Section One provides a brief statement of the problem and its solution. Section Two works through the solution for a special case that often comes up in practice. I also work through a concrete example chosen for its near-ubiquity in neuroscience, the equivalent circuit model of a patch of neuronal membrane. Section Three contains a simple derivation of the general solution given in Section One. The manuscript presupposes a little knowledge of first-year calculus, much of which is reviewed when needed.