GALACTIC DYNAMICS

1) Overview of the properties of galaxies: Morphology. Photometry. Kinematics. Scaling relations.
2) Potential theory: Gravitational potential. Poisson equation. Laplace equation. Gauss theorem. Potential energy. Potential energy tensor. Spherical systems. Newton theorems. Point mass. Homogeneous sphere. Hubble density profile. Power-law density profile. Axisymmetric systems. Logarithmic potential.
3) Orbits of the stars: Costants and integrals of the motion. Surfaces of section. Orbits in a static spherical potential. Orbits in a Keplerian potential. Orbits in a static axisymmetric potential. Motion in the meridional plane. Nearly circular orbits. Epicyclic approximation. Orbits in a two-dimensional non-axisymmetric non-rotating potential. Loop and box orbits. Stable and unstable orbits. Orbits in a two-dimensional nonaxisymmetric rotating potential. Jacobi integral. Lagrangian points. Corotation. Families of orbits x1, x2, x3, x4. Introduction to the orbits in a three-dimensional triaxial potential.
4) Collisionless systems: Geometric collisions. Strong collisions. Weak collisions. Crossing time. Relaxation time. Distribution function. Collisionless Boltzmann equation. Continuity equation. Euler equation. Jeans equations. Applications of the Jeans equations. Velocity ellipsoid. Asymmetric drift. Mass density in the Solar neighborhood. Velocity dispersions in spherical systems. Mass-anisotropy degeneracy. Spheroidal systems with isotropic velocity dispersions. Disk heating mechanisms. Virial theorem. Mass-to-light ratio of spherical systems. Rotation of elliptical galaxies. Jeans' theorem. Density profile from the distribution function. Spherical systems with isotropic velocity dispersion. Polytropes. Plummer sphere. Isothermal sphere. Singular isothermal sphere. King radius. King method to derive the mass-to-light ratio. King models. Tidal radius. Concentration parameter. Distribution function from the density profile. Eddington equation. Introduction to spherical systems with anisotropic velocity dispersion. Michie models.