Relationship between rotation curves and matter distribution in spiral
  galaxy discs
  Feng & Gallo (2011) developed a numerical method of deriving rotation curves
from the density distribution and, in particular, the inverse problem while
considering just a self-gravitating disc and the thin disc approximation. Our
first aim here is to reproduce the same analysis and expand it with various
ideas and examples. The main obstacles to building this numerical
implementation are certain singularities. We try to fix the instabilities using
different methods. Moreover, we add a final chapter extending the problem and
its method to a third dimension through the perpendicular to the galactic
plane.
  The dark halo (whose density is usually represented by a nearby spherical
distribution) is supposed to support the outer parts of the rotation curves of
spiral galaxies. Here, however, we work only with a self-gravitation disc. To
treat this topic we first calculate the disc density distribution from measured
rotation curve data of the Milky Way. We then compare this distribution with
the observed exponential stellar density, and the difference is attributed to a
dark disc. This representation of Feng & Gallo of the Galaxy with a dark disc
instead of a dark halo is controversial.
  When we analyse the effect of flares on rotation curves, the thin disc
approximation fails, and we need to introduce a vertical dimension to measure
and predict the effects of the flare through different heights. Just by
spreading the mass perpendicularly to the plane -- without adding any further
mass -- the flare provokes no severe changes on the rotation curve. The flare
mainly provokes a faster velocity decrease in the outer part of the Galaxy
($r\gtrsim 14$ kpc). But we also have obtained a slight velocity increase in
the first kiloparsecs after the starting point of the flare.
