Lecture 6: Introduction to stellar dynamics. II

Orbits in spherical potentials:

Binney and Tremaine 3.1 (new), 3.1 (old) 

For discussions of orbits in spherical potentials, you can also look at just
about any undergraduate mechanics book.

Integrals of motion:

Binney & Tremaine  3.1.1 (new), 3.1.1 (old)

Fluid mechanics:

Binney & Tremaine, Appendix F (new), Appendix 1.E (old)

The best derivation of the equations of fluid mechanics is Landau
and Lifshitz, Fluid Mechanics. Everything you need is derived
by page 4!

Collisionless Boltzmann equation:

Binney & Tremaine 4.1 (new), 4.1 (old)

The reason for using the cumbersome name "collisionless Boltzmann
equation" rather than the simple "Vlasov equation" is described
here