In a magnetic resonance apparatus having an RF radiating coil and gradient coils, and in a method for operating such a magnetic resonance apparatus, a pulse sequence, composed of multiple time steps, is specified for operating the gradient coils to time-dependently select regions of a selected slice of a selected volume of a subject. A non-linear equation system is then solved to obtain feed parameters for individual channels of the transmit coil for each time step, with specification of a desired target magnetization, and dependent on the pulse sequence specified for the gradient coils. The non-linear equation system is based on discrete values for time and space variable and, in addition to equations resulting from the Bloch equation, which are non-linear in their feed parameters, includes at least one additional equation that describes boundary conditions for the examination of the subject.