Elements of probability theory – random variables – Gaussian distribution – stochastic processes – characterizations and properties – Gauss-Markov processes – Brownian motion process – Gauss-Markov models – Optimal estimation for discrete-time systems – fundamental theorem of estimation – optimal prediction. Optimal filtering – Weiner approach – continuous time Kalman Filter – properties and implementation – steady-state Kalman Filter – discrete-time Kalman Filter – implementation – sub-optimal steady-state Kalman Filter – Extended Kalman Filter – practical applications.

Radiation-matter interaction – Sources of high energy (UV-gamma rays) radiation in the universe – Detectors for high energy particles, X-rays, gamma rays and neutrinos – Space astronomy – Elements of General Relativity – compact stars – magnetospheric processes around neutron stars (pulsars and magnetars) – interacting binaries – Roche potential and accretion – Shkura-Sunyaev thin disk model – accretion phenomenology around compact objects – stellar mass black holes vs supermassive black holes – AGN phenomenology and unified scheme – Jet production and superluminal motion – Supernova remnan

Occurrence and state of cosmic diffuse matter – ionized, atomic, molecular gas and dust – heating and cooling, equilibrium phases – probes of diffuse matter (line and continuum radiations at various wavelengths) – Thermal and ionization equilibrium of HII regions – UV shielding in molecular gas – extinction/reddening/polarization due to dust – dust heating and IR emission – star forming regions - cosmic rays and non-thermal synchrotron emission – recombination and re-ionization of IGM – Lyman alpha forest, Mg absorption systems – Gunn Peterson effect – Heating of intracluster gas – Sunyaev-

Conservation laws – Euler’s Equations – Common Equations of State – Hydrostatic Equiibrium – Isothermal sphere – Virial Theorem – linear perturbation theory – acoustic waves – Jeans’ instability – Rayleigh Taylor instability – de Laval nozzle – Parker wind solution – Bondi accretion – Shock waves – Sedov solution – elements of plasma physics – Debye screening – orbit theory – elements of MHD – flux freezing – Alfven waves – Langmuir oscillations – dispersion relation of electromagnetic waves propagating in plasmas – plasma instabilities – transport phenomena.

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Information Not AvailableCCD characterisation, Orbit maker and Virtual Observatory, Night sky observations ( Polar alignment of an astronomical telescope, Estimating atmospheric extinction in different colours (filters), measuring period of binary, imaging star clusters with various filters and plotting on H-R diagram, Distance determination to Cepheid variables based on their light curves, Classification of stars based on their spectra and the use of spectral classification in deriving distances to stars, etc).