This book shows cognitive scientists in training how mathematics computer science and science
can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on
mathematics for cognitive scientists and includes the mathematics and computational tools
needed to understand how to compute the terms in the Fourier series expansions that solve the
cable equation. The latter is derived from first principles by going back to cellular biology
and the relevant biophysics. A detailed discussion of ion movement through cellular membranes
and an explanation of how the equations that govern such ion movement leading to the standard
transient cable equation are included. There are also solutions for the cable model using
separation of variables as well an explanation of why Fourier series converge and a
description of the implementation of MatLab tools to compute the solutions. Finally the
standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using
MatLab.
