  A large population of ultra-diffuse galaxies (UDGs) was recently discovered
in the Coma cluster. Here we present optical spectra of three such UDGs, DF7,
DF44 and DF17, which have central surface brightnesses of $\mu_g \approx
24.4-25.1$ mag arcsec$^{-2}$. The spectra were acquired as part of an ancillary
program within the SDSS-IV MaNGA Survey. We stacked 19 fibers in the central
regions from larger integral field units (IFUs) per source. With over 13.5
hours of on-source integration we achieved a mean signal-to-noise ratio (S/N)
in the optical of $9.5$\AA$^{-1}$, $7.9$\AA$^{-1}$ and $5.0$\AA$^{-1}$,
respectively, for DF7, DF44 and DF17. Stellar population models applied to
these spectra enable measurements of recession velocities, ages and
metallicities. The recession velocities of DF7, DF44 and DF17 are
$6599^{+40}_{-25}$km/s, $6402^{+41}_{-39}$km/s and $8315^{+43}_{-43}$km/s,
spectroscopically confirming that all of them reside in the Coma cluster. The
stellar populations of these three galaxies are old and metal-poor, with ages
of $7.9^{+3.6}_{-2.5}$Gyr, $8.9^{+4.3}_{-3.3}$Gyr and $9.1^{+3.9}_{-5.5}$Gyr,
and iron abundances of $\mathrm{[Fe/H]}$ $-1.0^{+0.3}_{-0.4}$,
$-1.3^{+0.4}_{-0.4}$ and $-0.8^{+0.5}_{-0.5}$, respectively. Their stellar
masses are $3$-$6\times10^8 M_\odot$. The UDGs in our sample are as old or
older than galaxies at similar stellar mass or velocity dispersion (only DF44
has an independently measured dispersion). They all follow the well-established
stellar mass$-$stellar metallicity relation, while DF44 lies below the velocity
dispersion-metallicity relation. These results, combined with the fact that
UDGs are unusually large for their stellar mass, suggest that stellar mass
plays a more important role in setting stellar population properties for these
galaxies than either size or surface brightness.
