Methods of treating the Boltzmann equation for the case of a sinusoidally distributed source of fast neutrons in a material containing hydrogen are discussed and compared. The effects of the simplifying assumptions commonly employed in reactor calculations are analyzed. A technique which is particularly suitable for accurate numerical integration of the Boltzmann equation in the above case is described. Numerical results are being obtained by this method, and will be presented and compared with results obtained from other approximate methods in a subsequent paper.