  The Hermite-Taylor method, introduced in 2005 by Goodrich, Hagstrom and
Lorenz, is highly efficient and accurate when applied to linear hyperbolic
systems on periodic domains. Unfortunately its widespread use has been
prevented by the lack of a systematic approach to implementing boundary
conditions. In this paper we present the Hermite-Taylor Correction Function
method, which provides exactly such a systematic approach for handing boundary
conditions. Here we focus on Maxwell's equations but note that the method is
easily extended to other hyperbolic problems.
