  We present results from sensitive, multi-epoch NuSTAR observations of the
late-type star-forming galaxy M83 (d=4.6 Mpc), which is the first investigation
to spatially resolve the hard (E>10 keV) X-ray emission of this galaxy. The
nuclear region and ~ 20 off-nuclear point sources, including a previously
discovered ultraluminous X-ray (ULX) source, are detected in our NuSTAR
observations. The X-ray hardnesses and luminosities of the majority of the
point sources are consistent with hard X-ray sources resolved in the starburst
galaxy NGC 253. We infer that the hard X-ray emission is most likely dominated
by intermediate accretion state black hole binaries and neutron star low-mass
X-ray binaries (Z-sources). We construct the X-ray binary luminosity function
(XLF) in the NuSTAR band for an extragalactic environment for the first time.
The M83 XLF has a steeper XLF than the X-ray binary XLF in NGC 253, consistent
with previous measurements by Chandra at softer X-ray energies. The NuSTAR
integrated galaxy spectrum of M83 drops quickly above 10 keV, which is also
seen in the starburst galaxies NGC253, NGC 3310 and NGC 3256. The NuSTAR
observations constrain any AGN to be either highly obscured or to have an
extremely low luminosity of $_{\sim}^<$10$^{38}$ erg/s (10-30 keV), implying it
is emitting at a very low Eddington ratio. An X-ray point source consistent
with the location of the nuclear star cluster with an X-ray luminosity of a few
times 10$^{38}$ erg/s may be a low-luminosity AGN but is more consistent with
being an X-ray binary.
