We study the explicitly time-dependent response of a razor-thin axisymmetric disc to externally imposed perturbations by recasting the linearized Collisionless Boltzmann equation as an integral equation and applying Kalnajs' matrix method As an application we consider the idealized problem of calculating the dynamical friction torque on a steadily rotating, two-dimensional bar. We consider two choices of basis functions in the matrix method, showing that both lead to comparable results. The torques from our linearised calculation are in excellent agreement with those measured from N -body simulation, as long as the bar perturbation does not resonate with a significant fraction of the disc's stars.