  The moment method is applied to the quantum theory for a trapped dilute gas,
obtaining equations for the evolution of the cloud. These equations proof the
existence of undamped oscillations in a two-dimensional harmonic trap with
radial symmetry. In all other cases we can, with physically reasonable
approximations, solve the equations and find the frequencies of the collective
modes for all temperatures, from the pure Bose-Einstein condensate up to the
normal gas.
