What is kinetic theory? I am taking a course on fluid dynamics right now, and I have been wondering about one thing for some time now. We have three ways to look at a gas ($N$ particles):
1) Microscopic: The state (position and velocity) of each particle is known at every point of time. Evolution of the state is determined by Newton.
2) Kinetic: We have a distribution function f (as the solution of the Boltzmann-equation) of the particles. We have derived the Boltzmann equation by using Heuristic arguments and Newton.
3) Macroscopic: Looking at macroscopic quantities.
Is this correct? And is the essence of the kinetic view the fact that we have a distribution function and an evolution equation for that? Especially in contrast to the microscopic view? In addition, I wrote down the word "continuum" next to kinetic in my lecture notes but can't make sense of that.
And another question: We derived the macroscopic view from the kinetic view, but i am not so sure about the relation between the microscopic view and the kinetic view.