Time-stepping: different schemes.

Force calculations: direct summation, tree algorithms, mesh-based methods.

Gravitational potential. General results.

Potentials of spherically symmetric systems.

Potentials of non-spherically systems:
trends and general results.

Motion of particles in a central force: basic equations and properties. Epicycle approximation. Types of orbits. Integrals of motion. Resonances.

Virial theorem

Two-body scattering. Dynamical friction. Violent relaxation.

Distribution function. Jeans equations. Asymmetric drift.

Eulerian and Lagrangian equations

Bernoulli equation. Kelvin circulation theorem.

Acoustic waves. Jeans instability. Dispersion relation.

Shock adiabatic. Strong shocks. Sedov solution. Waves in inhomogeneus atmosphere. Oblique shock.

Toomre instability. Convection. Kelvin-Helmholtz Cooling instability. Bar Instability.