Along the way you learn about the calculus of variations which allows you to find relationships that maximize or minimize quantities. You then apply the new formulation to several types of motion including classical planetary motion. After an interesting look at Newtonian motion in accelerated reference frames, the course winds up with studies of rigid rotation and coupled oscillation. Gas pressure depends on the behavior of gas atoms. Gas pressure on the walls of a container is caused by the average force gas atoms exert as they collide with the container walls.
Statistical mechanics leads to a quantitative relation between gas pressure and atomic properties.
In this course statistical mechanics is applied to two important cases. The principles of statistical mechanics can be used to derive thermodynamic equations of state. They also lead to profound insights into the meaning of thermodynamic quantities like temperature and entropy. When you study statistical mechanics on the spiral staircase physics curriculum, you return to thermodynamics at a higher level. Your upward journey along the physics curriculum spiral staircase has brought you to electromagnetism at the junior-senior level.