  Observations of the frequency dependence of the global brightness temperature
of the redshifted 21 cm line of neutral hydrogen may be possible with single
dipole experiments. In this paper, we develop a Fisher matrix formalism for
calculating the sensitivity of such instruments to the 21 cm signal from
reionization and the dark ages. We show that rapid reionization histories with
duration delta z< 2 can be constrained, provided that local foregrounds can be
well modelled by low order polynomials. It is then shown that observations in
the range nu = 50 - 100 MHz can feasibly constrain the Lyman alpha and X-ray
emissivity of the first stars forming at z = 15 - 25, provided that systematic
temperature residuals can be controlled to less than 1 mK. Finally, we
demonstrate the difficulty of detecting the 21 cm signal from the dark ages
before star formation.
