For a conservative force, the infinitesimal work is an exact differential. A non-conservative force is one for which the work done depends on the path

For a single-particle system, the difference of potential energy is the opposite of the work done by the forces acting on the particle as it moves from one position to another The potential energies for Earth’s constant gravity, near its surface, and for a Hooke’s law force are linear and quadratic functions of position, respectively

potential energy — function of position, energy possessed by an object relative to the system considered. exact differential — is the total differential of a function and requires the use of partial derivatives if the function involves more than one dimension. force — conservative if the work done over any closed path is zero. Hooke’s law force — linear and quadratic functions of position, respectively.