Elements of probability theory - random variables-G aussian distribution-stochastic processes- characterizations and properties-Gauss-Markov proce sses-Brownian motion process-Gauss- Markov models - Optimal estimation for discrete-tim e 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 Filt er-Extended Kalman Filter-practical applications.

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

Occurrence and state of cosmic diffuse matter – ion ized, atomic, molecular gas and dust – heating and cooling, equilibrium phases – probes of diffuse matter (line and continuum radiations at various wavelengths) – Thermal and io nization equilibrium of HII regions – UV shielding in molecular gas – extinction/reddening/p olarization due to dust – dust heating and IR emission – star forming regions - cosmic rays and n on-thermal synchrotron emission – recombination and re-ionization of IGM – Lyman alph a forest, Mg absorption systems – Gunn Peterson effect – Heating of intracluster gas – Sun

Conservation laws – Euler’s Equations – Common Equa tions of State – Hydrostatic Equiibrium – Isothermal sphere – Virial Theorem – linear pertu rbation theory – acoustic waves – Jeans’ instability – Rayleigh Taylor instability – de Lava l 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- plasm a instabilities - transport phenomena

CCD characterisation, Orbit maker and Virtual Obser vatory, 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 variable s based on their light curves, Classification of stars based on their spectra and the use of spec tral classification in deriving distances to stars, etc)