Basic concepts and mathematical issues: oscillation mode, radial and non-radial pulsations,
spherical harmonics, basic coordinate systems and transformations between them, the
Eulerian and Lagrangian description, perturbation of the surface element and its normal.
Types of pulsating variables: stellar pulsations across the Hertzsprung-Russell diagram,
instability domains, basic properties of different types. Oscillation properties: the Lamb and
Brunt-Vaisala frequency, acoustic and gravitational modes, propagation diagrams, conditions
for trapping of modes, pulsation constant, period-luminosity relation. Mathematical
description of pulsations: general equations of hydrodynamics, linear non-radial non-
adiabatic pulsations, boundary conditions, adiabatic and quasi-adiabatic approximation,
Sturm-Liouville type problem, variational principle, asymptotic dispersion relations.
Excitation mechanism: Eddington valve mechanism, self-excitation (opacity) mechanism,
work integral, stochastic excitation by turbulent convection. Detection of pulsating stars:
Fourier methods, statistical methods, wavelet analysis. Observed characteristics and
identification of pulsation modes: light variations of a pulsating star, changes of radial
velocity, modelling of line profile variations, methods of the mode identification from
photometry and spectroscopy. Basic effects of rotation: advection, rotational splitting of
modes, Coriolis force, Ledoux constant, effects of moderate rotation, centrifugal force. Helio-
and Asteroseismology: seismic model of a star, the most important achievements of
helioseismology, examples of asteroseismic modelling.
