We report on the linear response density functional study of the magnetization dynamics in Co(100) film driven by a nonuniform magnetic field. At resonant frequencies in the terahertz range, the magnetic field excites standing spin waves of the system and the induced magnetization penetrates the whole volume of the film. The pattern of magnetization precession is strongly influenced by the spin-flip excitations of single electrons which lead to the Landau damping of the spin-wave modes. Our results pave the way for the precise control of terahertz magnetization dynamics in itinerant magnets.