Let be the angle which the Bloch vector makes with the -w axis. At resonance, is related to the Rabi frequency by the simple differential equation 
It is a simple matter to generalize this equation to a frequency off of resonance by replacing the Rabi frequency by the generalized Rabi frequency
The most general solution to this differential equation would therefore be
where . This equation is often referred to as the area theorem because it relates the area under the generalized Rabi frequency curve to the angle through which the Bloch vector rotates.