Collisionless Boltzmann Equation

This lecture covers the Collisionless Boltzmann equation, discussing topics such as the distribution function of stellar systems, the Jeans theorems, resonances in realistic bars, chaotic orbits, and the limitations of the equation. It also explores the relations between distribution functions and observables, the equilibria of collisionless systems, and the integrals of motion. The instructor explains the importance of velocity constraints, self-gravity, and perturbations in modeling galaxies, aiming for self-consistent solutions. Various coordinate systems and their implications on the equation are also discussed, along with the limits and assumptions of the Collisionless Boltzmann equation.