  We present the results of a kinematic analysis of red giants and subgiants
whose centroids are in the plane of our Galaxy. For this, the positions,
parallaxes, proper motions, and radial velocities of these stars from the
$Gaia$ EDR3 catalog were used. We applied two approaches to obtain kinematic
parameters. The first approach -- solving the equations of the
Ogorodnikov--Milne model with respect to 12 kinematic parameters -- is
generally accepted, but has a number of disadvantages. The second approach
developed by us is to find the components of galactocentric centroid's velocity
and their partial derivatives with respect to coordinates directly from
differential equations for the stellar velocity field. To calculate the
kinematic parameters by the methods mentioned above, same stellar samples were
used. From these samples spherical regions with a radius of 1 kpc were
selected, the centers of which were located strictly in the Galactic mid-plane
at the nodes of the coordinate grid ($x_{gal}$, $y_{gal}$) of a rectangular
Galactocentric coordinate system with step 100 pc. The region of the Galaxy
under study occupies the coordinate interval $115^\circ < \theta < 245^\circ$,
0 kpc$ < R < $16 kpc, -1 kpc$ < z < $1 kpc. We show the behavior of local
kinematic parameters as well as global parameters such as the circular velocity
of stars as a function of galactocentric coordinates. For the first time, the
components of centroids' spatial velocities and all their partial derivatives
as well as their behavior as a function of galactic coordinates have been
derived. The behavior of the $\partial V_R/\partial \theta$ and $\partial
V_\theta/\partial \theta$ parameters as a function of galactic coordinates has
been derived for the first time.
