  A simple closed-form analytic expression for the probability of two-flavour
neutrino oscillations in a matter with an arbitrary density profile is derived.
Our formula is based on a perturbative expansion and allows an easy calculation
of higher order corrections. The expansion parameter is small when the density
changes relatively slowly along the neutrino path and/or neutrino energy is not
very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our
approximation is not equivalent to the adiabatic approximation and actually
goes beyond it. We demonstrate the validity of our results using a few model
density profiles, including the PREM density profile of the Earth. It is shown
that by combining the results obtained from the expansions valid below and
above the MSW resonance one can obtain a very good description of neutrino
oscillations in matter in the entire energy range, including the resonance
region.
