Hi there:
I would like to ask you if it is possible to obtain the mathematical representation of a DC motor using a potentiometer connected to the motor shaft and Arduino UNO board.

Technical Parameters:
the potentiomer can be turned from 0 to 300 degrees.
DC motor voltage 7V.
Arduino UNO board.
Motor shield.

Yeah ! exactly ! what? What do you mean by "mathematical representation"? Points have mathematical representations. Lines, surfaces, etc. have mathematical representations. Cars, planes, boats, and motors do not.

I would like to ask you if it is possible to obtain the mathematical representation of a DC motor using a potentiometer connected to the motor shaft and Arduino UNO board.

Probably not, way to vague idea of what you are seeking.

zaciatok:
is possible to obtain the mathematical representation of a DC motor

I originally assumed you want to mathematically describe the relationship between the pot and the motor's RPM (i.e., speed control), but not if you are going to connect the pot directly to the motor's shaft...