  We present the first asymmetric drift (AD) measurements for unresolved
stellar populations of different characteristic ages above and below 1.5 Gyr.
These measurements sample the age-velocity relation (AVR) in galaxy disks. In
this first paper we develop two efficient algorithms to extract AD on a
spaxel-by-spaxel basis from optical integral-field spectroscopic (IFS)
data-cubes. The algorithms apply different spectral templates, one using simple
stellar populations and the other a stellar library; their comparison allows us
to assess systematic errors in derived multi-component velocities, such as
template-mismatch. We test algorithm reliability using mock spectra and Monte
Carlo Markov Chains on real data from the MaNGA survey in SDSS-IV. We quantify
random and systematic errors in AD as a function of signal-to-noise and stellar
population properties with the aim of applying this technique to large subsets
of the MaNGA galaxy sample. As a demonstration of our methods, we apply them to
an initial sample of seven galaxies with comparable stellar mass and color to
the Milky Way. We find a wide range of distinct AD radial profiles for young
and old stellar populations.
