$\Lambda$CDM Cosmology for Astronomers
  The homogeneous, isotropic, and flat $\Lambda$CDM universe favored by
observations of the cosmic microwave background can be described using only
Euclidean geometry, locally correct Newtonian mechanics, and the basic
postulates of special and general relativity. We present simple derivations of
the most useful equations connecting astronomical observables (redshift, flux
density, angular diameter, brightness, local space density,...) with the
corresponding intrinsic properties of distant sources (lookback time, distance,
spectral luminosity, linear size, specific intensity, source counts,...). We
also present an analytic equation for lookback time that is accurate within
0.1% for all redshifts $z$. The exact equation for comoving distance is an
elliptic integral that must be evaluated numerically, but we found a simple
approximation with errors $< 0.2$% for all redshifts up to $z \approx 50$.
