Few Cycle Optical Pulse Propagation: a detailed calculation Paul Kinsler Department of Physics, Imperial College, Prince Consort Road, London SW7 2BW, United Kingdom. http://arXiv.org/physics/0212014 This document contains my detailed calculation of the Generalised Few-cycle Envelope Approximation (GFEA) propagation equation reported and used in Phys. Rev. A (submitted) and its associated longer version at arXiv.org/physics/0212016. This GFEA propagation equation is intended to be applicable to optical pulses only a few cycles long, a regime where the standard Slowly Varying Envelope Approximation (SVEA) fails. Email: Dr.Paul.Kinsler@physics.org