Efficient ion-cyclotron heating in tokamak plasmas is effectively localized in the central region of the plasma, near the ion second-harmonic layer in a single ion species plasma, or near the ion-ion hybrid layer in a plasma containing a minority ion species. The fast Alfven wave (FAW), which carries the incident rf power, from the low magnetic-field side, is generally focused in (by antenna design and propagation) toward this central region on the equatorial plane of the tokamak plasma. There the FAW encounters a "coupling" region and may undergo reflection (R), transmission(T)-to the high magnetic field side, mode conversion (C)-to an ion-Bernstein wave (IBW), and kinetic dissipation (D)-due to Doppler-shifted ion-cyclotron damping. (Here we ignore electron TTMP and/or Landau damping; these can be readily included by expanding on our formalism.) To determine these power transfer coefficients (R, T, C and D) the problem is in general formulated as an integro-partial-differential equation based upon the linearized Vlasov-Maxwell equations for an inhomogenous plasma. This is however difficult to solve, even numerically, and has been usually approximated by a fourth or sixth-order o.d.e. description which is amenable to numerical integration.