Abstract

Electrical activity is central to the workings of various physiological systems including the nervous system and the heart.
Given its importance and its quantitative nature, electrophysiology has long been a central subject in mathematical biology. In this course, we shall cover some of the fundamental concepts and models in mathematical electrophysiology. After discussing the fundamentals of the membrane potential and membrane channels, we will talk about cell volume control and the pump-leak model. After this, we will discuss the Hodgkin-Huxley model, the FitzHugh-Nagumo model and action potential propagation. Finally, we will discuss the bidomain equation
for cardiac electrical activity. This is a lot of material for a few days, and we attempt an overview that will guide the interested attendee for further study into this active and important area.