The transfer matrix for the neutron flux in slab geometry is expressed analytically, along with a number of auxiliary quantities, for energy-independent interactions with isotropic scattering. The eigenvalues and eigenfunctions of the transfer matrix are readily expressed in terms of those introduced by Case, working directly with the Boltzmann equation. The results are applied to the albedo problem, the Milne problem, and the critical slab problem. Since the transfer matrix approach works in principle for any cross sections, the ease of application implies that numerical calculations for more complicated cross sections will be reasonably straightforward.