  We give an improved formalism for calculating the evolution of density
fluctuations and temperature perturbations in flat universes. Our equations are
general enough to treat the perturbations in collisionless relics like massive
neutrinos. We find this formulation to be simpler to use than gauge dependent
and other gauge-invariant formalisms. We show how to calculate temperature
fluctuations (including multipole moments) and transfer functions, including
the case of collisionless relics like massive neutrinos. We call this formalism
"quasi-Newtonian" because the equations for the potential and cold matter
fluctuation evolution have the same form as the Newtonian gravitational
equations in an expanding space. The density fluctuation variable also has the
same form inside and outside of the horizon which allows the initial conditions
to be specified in a simple intuitive way. Our sample calculations demonstrate
how to use these equations in cosmological models which have hot, cold, and
mixed dark matter and adiabatic (isentropic) or isocurvature modes. We also
give an approximation which may be used to get transfer functions quickly.
