Electroencephalography (EEG) and magnetoencephalography (MEG) are non-invasive methods of studying the functional activity of the human brain with millisecond temporal resolution. Much of the work in EEG and MEG in the last few decades has been focused on estimating the properties of the internal sources of the fields from the external measurements, i.e. on solving the inverse problem of EEG and MEG. To handle this task one must first study the forward problem, i.e. how the fields arise from a known source. For practical purposes, one also has to choose appropriate models for the source and the head as a conductor. The most straightforward model for describing the surface evoked potential or the external evoked magnetic field is the single equivalent current dipole. In EEG models the volume conductor properties of the head are commonly modelled by three or four concentric spherical shells with different electrical conductivities representing the brain, the cerebrospinal fluid, the skull, and the scalp. While more accurate geometric models have been applied, such asymmetric models are limited in accuracy by knowledge of boundaries and resistivities of various tissues. In this article we consider a three-layer spherical volume conductor model and calculate the dipole-induced potential by analytical methods. This calculation requires the symbolic solution of a system of linear equations which is not complicated but that would be a pain when done by pencil and paper. We use Maple for setting up the system of model equations, solve it symbolically, and then generate numerical code to obtain a fast program for the evaluation of the potential. Finally, the dipole-envoked electric potential is plotted for realistic EEG model parameters
