**IIAP Syllabus 2022 PDF**: IIAP Syllabus and Exam Pattern PDF are available on this page for Download. The Indian Institute of Astrophysics has released the Subject Wise **IIAP Junior technical assistant (electronics), Junior research assistant (observations), Mechanic, Engineer trainee (IT support), and Research trainee (Optics) Syllabus** on its Official website @ **iiap.res.in**. The IIAP Notification 2022 has been released by the Officials and the IIAP Exam 2022 will be held soon. So the Candidates who had applied for IIAP 2022 and Stated Exam preparation for the IIAP Exam should check this Article now. Here we have provided the **IIAP Syllabus.** The IIAP Exam will be conducted to recruit the Posts. To help the Aspirants we have uploaded the IIAP Syllabus on this page for Download. Here we have provided the Subject Wise IIAP Syllabus PDF.

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**Download IIAP Syllabus 2022 PDF**

**Detailed Syllabus for integrated M.Sc-Ph.D program**

**Mathematical Methods**

Vector space and matrices, linear independence, bases dimensionality, Inner product, tensors, transformations of, parallel transport, linear transformation matrices, inverse, orthogonal and unitary matrices, independent element of a matrix, Eigen values and Eigen vectors, diagonalization, complete orthonormal sets to functions, series, convergence tests; complex Variables, Cauchy- Riemann condition, analytic functions, Cauchy’s theorem, Cauchy integral formula, Laurent series, singularities, residue theorem, contour integration, evaluation of definite integrals. Differential equations, second order linear ODEs with variable coefficients, Solution by series expansion, non-homogeneous differential equations and solution by the method of Green’s functions with applications. Eigenvalue methods, up to Strum-Liouville systems. Special functions, Legendre, Bessel, Hermite and Laguerre functions with their physical applications, generating functions, orthogonality conditions, recursion relations, Integral transforms, Fourier integral and transforms, inversion theorem, Fourier transform of derivatives, convolution theorem, Laplace Transform(LT), LT of Derivatives, Inverse LT, Fourier series; properties and applications, discrete Fourier transform.

**Classical Mechanics**

Preliminaries, Newtonian mechanics of one and many-particle systems, conservation law, constraints and their classification, principle of virtual work, generalized coordinates, D’Alembert’s principle and Lagrange’s equations, velocity-dependent potentials and the dissipation function, simple applications of the Lagrangian formulation, Hamilton’s principle, Lagrange’s equations from Hamilton’s principle, conservation theorems and symmetry properties, energy function and the conservation of energy. The Hamiltonian formation of mechanics, Legendre transformations and the Hamilton’s equations of motion, cyclic coordinates and conservation theorems, Hamilton’s equations from Hamilton’s principle, the principle of least action, canonical transformations with examples, the harmonic oscillator, Poisson’s brackets, equations of motion and conservation theorems in the Poisson Bracket formulation.

Hamilton-Jacobi(HJ) theory and action -angle variables, the HJ equation for Hamilton’s principal function, Harmonic oscillator as a example of the HJ method, the HJ equation for Hamilton’s characteristic function, separation of variables in the HJ equation and the action-angle variables. Non-linear dynamics: dynamical systems, ergodicity, and chaos theory. The Central force problem, two-body problem and its reduction to the equivalent one-body problem, the equations of motion and first integrals, the equivalent one-dimensional problem and classification of orbits, the differential equation of the orbit, closure and stability of orbits, the Kepler problem , scattering in a central force field, Rutherford scattering, transformation of the scattering problem to laboratory coordinates, the three-body problem.

Rigid body dynamics, the Euler angles, Euler’s on the motion of a rigid body, rate of change of a vector, the Coriolis force, angular momentum and kinetic energy of motion about a point, the Euler equations of motion of rigid bodies, precession, tidal interaction. Formulation of the problem of small oscillations, the eigenvalue equation and the principal axis transformation, frequencies of free vibration and normal coordinates. Stability studies in astrophysical situations.

**Quantum Mechanics**

Inadequacy of classical mechanics, Schrödinger equation, continuity equation, Ehrenfest theorem, admissible wave functions, stationary states, one-dimensional problems; walls and barriers, Schrödinger equation for harmonic oscillator and its solution, uncertainty relations, states with minimum uncertainty product.

Super position principle, general formalism of wave mechanics, commutation relationship, representation of states and dynamical variables, completeness of Eigen functions, Dirac-delta function, Bra & Ket notation, matrix representation of an operator, harmonic oscillator and its solution by matrix method, Heisenberg equation of motion.

Angular momentum in quantum mechanics, commutation relationships, Eigen values, spin angular momentum, Pauli’s matrices, addition of angular momentum, Clebsch-Gordon coefficients, Wigner-Eckart theory.

Central force problem, spherically symmetric potentials in three dimensions, separation of wave equation, parity, three-dimensional square-well potential and energy levels, the hydrogen atom; solution of the radial equation, energy levels and stationery state wave functions, discussion of bound states, degeneracy.

Time-independent perturbation theory, non-degenerate case, first order and second perturbations with the example of an oscillator, degenerate cases, removal of degeneracy in second order, Zeeman effect without electron spin, first-order Stark effect in Hydrogen, perturbed energy levels, occurrence of permanent electric dipole moments.

Time-dependent perturbation theory, Fermi’s golden rule. Transition probability.

**Electronics**

Kirchhoff’s Laws, KCL, KVL and their limitations, classification of devices of an electrical circuit, basic devices, resistors, controlled sources, diodes, capacitors and inductors, ideal transformers, basic circuit analysis methods, nodal, mesh and modified nodal-analysis, transient analysis of RL, RC and RLC circuits, network theorems, Tellegen’s theorem, superposition theorem, Thevenin-Norton theorem, substitution theorem, reciprocity theorem, maxpower-transfer theorem, star-delta- transformation, steady state sinusoidal analysis: phasors, phasor diagrams, power in ac circuits, network analysis methods and network theorems recalled, polyphase circuits, circuits with ideal transformers.

Introduction to operational amplifiers, the difference amplifier and the ideal operational amplifier models, concept of negative feedback and virtual short; Analysis of simple operational amplifier circuits; Frequency response of amplifiers, Bode plots, feedback, feedback topologies and analysis for discrete transistor amplifiers, stability of feedback circuits using Barkhausen criteria.

Linear applications of operational amplifiers, instrumentation and isolation amplifiers, current and voltage sources, active filters, introduction to Boolean algebra and switching functions, Boolean minimization, finite-state machines, design of synchronous FSMs, FSM minimization, synchronous FSMs, bipolar Logic Families (TTL + ECL), MOS logic families (NMOS and CMOS), and their electrical behaviour, memory elements, timing circuits, Elementary combinational and sequential digital circuits, adders, comparators, shift registers, counters, logic implementation using programmable devices (ROM,PLA,FPGA).

**Physics Lab**

- Measurement of Earth’s Magnetic Field using Hall effects probe.

2. Study of black body radiation and verification of Wien’s law using prism based spectrometer.

3. Determination of wavelengths of H and He spectra using grating based spectrometer.

4. Measurement of universal gravitational constant using torsional balance.

5. Determination of charge of an electron using Milkon’s oil drop method.

6 Verification of Coulomb’s law.

7. Verification of Faraday’s law of induction and Lenz’s law using variable gap magnet and induction coil.

8. Determination of speed of light in air by Focult’s rotating mirror.

9. measurement of charge to mass ratio (e/m) of an electron using Helmholtz coil.

10. Hall Effect

11. Band gap measurements with four probe method

**Statistical Physics**

Review of basic thermodynamics, foundation of statistical mechanics : macroscopic and microscopic states, contact between statistics and thermodynamics, physical significance of (N, V, E), the classical gas, entropy of mixing and Gibb’s paradox, phase space of classical system, Liouville`s theorem and its consequences, quantum states and phase space; elements of ensemble theory – a system in microcanonical, canonical, and grand canonical ensembles, partition functions, physical significance of statistical quantities, example of classical system, energy and energy-density fluctuations and mutual correspondence of various ensembles; formulation of quantum statistics – quantum mechanical ensemble theory, Density matrix, statistics of various quantum mechanical ensembles, system composed of indistinguishable particles, theory of simple gases – ideal gas in various quantum mechanical ensemble, Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac distributions, statistics of occupation number, mono-atomic and diatomic gases composed of particles with internal motion; ideal Bose and Fermi gases – thermodynamics behavior of and ideal Bose gas, Bose-Einstein condensation and, elementary excitations in liquid helium II, thermodynamic behaviour of an ideal Fermi gas, the electron gas, non-relativistic and relativistic degenerate electron gas, theory of white dwarf stars; cooperative phenomena: electric and magnetic properties of matter: Curie and Curie-Weiss Laws, Pauli paramagnetism, Exchange interaction and the origin of internal fields:para, ferro and anti ferro states of matter; Boltzmann transport theory, H theorem, calculation of kinetic coefficients, elementary concepts of plasma kinetic theory; fluctuations: thermodynamic fluctuations, Brownian motion, Einstein and Lengevin theory of Brownian motion.

**Nuclear and Particle Physics**

Radioactive decay, sub-nuclear particles, binding energies, nuclear forces, pion exchange, Yukawa potential, isospin, neutron and proton, Deuteron, shell model, magic numbers, nuclear transitions, selection rules, liquid drop model, collective excitations, nuclear fission and fusion, beta decay, neutrinos. Fermi theory, parity violation.

Introduction to particle physics, astrophysical applications of nuclear, and particle physics, particle acceleration in astrophysics, pair plasmas, cosmic rays, TeV gamma rays, neutrino astrophysics.

**Atomic and Molecular Physics**

Systematics of atomic states, genesis of the periodic system of elements, many-electron systems, L-S coupling, Hartree-Fock approximation. Perturbations, level splittings, and term diagrams, spectroscopic terms, parity, spin orbit coupling, Zeeman effect, hyperfine structure, radiative transitions, dipole approximation, oscillator strengths, selection and transition rules, line broadening mechanisms, Doppler, natural, and collisional broadening, molecular structure, Born-Oppenheimer approximation, electron binding of nuclei, H2, H2+, rotation spectra, rotation and vibration spectra, electronic-rotation-vibration spectra.

**Electrodynamics**

Electrostatics and magnetostatics, special techniques. Maxwell’s equations, vector and scalar potentials and the wave equation, Gauge transformations, Lorenz gauge, Coulomb gauge, Green’s function for the wave equation, four-vectors, mathematical properties of the space-time in special relativity, matrix representation of Lorentz transformation, covariance of electrodynamics, transformation of electromagnetic fields.

**Electronics Lab**

- Analog electronics:

RLC circuits, maximum power transfer theorem, power supplies- unregulated and regulated. Transistor amplifiers, multi vibrators. Operational amplifier circuits- adder, subtractor , multiplier, integrator and differentiator. Filters using OpAmps – low pass, high pass, band pass and band rejection. Oscillators, Introduction to ADC/DAC.

- Digital electronics:

Truth table verification of logic gates, half adder, full adder , subtractor. Function implementation using multiplexres, demultiplexers. Implementation of flip flops with universal gates – JKFF, DFF,TFF. Counters – Binary , BCD, Up/Down and modulo N counter, Registers.

**Astronomical Techniques**

Coordinate systems, precession, time, heliocentric corrections, methods of observation, resolution, sensitivity, noise, quantum efficiency, spectral response, Johnson noise, signal to noise ratio, background, aberrations, telescopes at different wavelengths, detectors at different wavelengths, imaging, spectroscopy, polarimetry, calibration, atmospheric effects at different wavelengths, active/adaptive optics, interferometry, speckle interferometry, aperture synthesis, neutrino astronomy, gravitational wave astronomy.

**Optics Lab**

**Numerical Techniques**

Methods of data reduction, Fourier transforms, calibrations, Numerical techniques in physics and astrophysics, errors and error propagation, numerical integration and interpolation, random numbers, astrostatistics, probability distributions, hypothesis testing, sampling methods, multivariate analysis, regression, time-series analysis, data reduction, error analysis, numerical solutions of algebraic, ordinary differential and partial differential equations.

**Fundamentals of Astrophysics**

Overview of major contents of universe, Black body radiation, specific intensity, flux density, luminosity, Basics of radiative transfer (Emission/absorption coefficients, source functions), Magnitudes, distance modulus, Color index, Extinction, Color temperature, effective temperature, Brightness temperature, bolometric magnitude/luminosity, Excitation temperature, kinetic temperature, Utility of stellar spectrum, basic knowledge of stellar atmospheres, Binaries, variable stars, clusters, open and globular clusters, Laws of planetary motion, Motions and Distances of Stars, Statistical and moving cluster parallax, Velocity Dispersion, Compact objects (BH-systems, Accretion rate/efficiency, Eddington luminosity), Shape, size and contents of our galaxy, Normal and active galaxies, High energy physics (introduction to X-ray and Gamma-ray radiation processes), Newtonian cosmology, microwave background, early universe.

**Radiative Processes**

Basics of theory of radiation field, thermal radiation, radiative diffusion, radiative transfer theory, elementary stellar atmospheres, relativistic electrodynamics, emission of electromagnetic radiation, scattering, Brehmstrahlung, synchrotron radiation, inverse-Compton process, plasma effects.

**Stellar Physics**

Introduction to stars: HR diagram, a discussion on the variety of stellar phenomena. Stellar Structure ( Kippenhahn & Weigert Chapters 1-10, supported by material from Bohm Vitensse Vol III, Chapters 2-7 ), stellar opacities, stellar polytropes, Energy Generation in Stars: Calculation of thermonuclear reaction rates for non-resonant and beta-decay reactions, The various reaction chains: pp-I, II, III, CNO, He-burning, C-burning, Si-burning, photo-dissociation (Clayton; some references to Arnett as well). Neutrino emission from Stars: The solar neutrino “problem” and its solution, terrestrial detection of stellar neutrinos – solar and supernovae (Arnett, Bahcall). Stellar degeneracy and Equations of State: Stellar degeneracy (Clayton), Chandrasekhar mass, EoS of matter at near-nuclear and nuclear densities (Shapiro & Teukolsky). Final stages of stellar evolution: Supernovae (a basic understanding of the core-collapse process and the structure of the progenitor) and neutron stars – a basic knowledge of NS structure, the problems associated with determining a unique equation of state for NS, various manifestations of NS. (Shapiro & Teukolsky, Arnett, various review articles wherever necessary).

**Fluids and Plasmas**

Basic equations of fluid mechanics, viscosity, gas dynamics, waves and instabilities, turbulence, orbit theory, elements of MHD, microscopic theories, Boltzmann and Vlasov equations, plasma oscillations, basic plasma phenomena, plasma oscillations; plasmas, definition and general properties, Debye shielding phenomenon and criteria for plasma, motion of charged particles in electromagnetic field; uniform E & B fields, Electric field drift, non-uniform magnetostatic field, gradient B drift, parallel acceleration and magnetic mirror effect, curvature drift, adiabatic invariants; fundamental equations of magneto-hydrodynamics(MHD), the MHD approximation, Hydromagnetic waves; magnetosonic and Alfven waves, magnetic viscosity and Reynolds number, diffusion of magnetic lines and frozen-in fields, concept of magnetic pressure, plasma confinement schemes, Waves in plasma, electron and ion plasma waves, their dispersion relations and properties, dynamo theory.

**Solid State Physics**

Einstein and Debye models of specific heat, thermal conductivity, effect of imperfections; electron states, electron in a periodic potential and the Bloch theorem, the free electron and tight binding approximations, energy bands and band structure of solids, band width, energy gap and Fermi surface; density of states and the total number of states, effective mass, electrons and holes, semimetal; free electron gas in three dimensions, specific heat, Sommerfeld theory of electrical conductivity, Wiedemann-Franz law, Hall effect, superconductivity, Meissner effect, type I and type II superconductors, heat capacity, London equation and penetration of magnetic field, Cooper pairs and the B C S ground state (qualitative).

Cold equation of state below neutron drip: Harrison-Wheeler, BPS, equation of state above neutron drip: BBP, many body theory, Hartree Fock, Bethe-Johnson, delta resonance, pion condensation, quark stars. Neutron star & white dwarf models: masses and radii. Cooling: structure of the surface layers of the white dwarf and cooling, free neutron decay, URCA rate, neutrino transparency , neutron star cooling. Superfluidity in neutron stars, pulsar glitches.

**Relativistic Quantum Mechanics**

Scattering, classical radiation field, creation, annihilation and number operators. Quantized radiation field, unified approach to emission, absorption, and scattering of photons by atoms, radiation damping and resonance fluorescence, dispersion relations and causality, relativistic wave equation (Klein- Gordon and Dirac equations), basics of quantum electrodynamics.

**Physical Optics**

Complex representation of waves, propagation of waves, diffraction, scalar diffraction theory, Fresnel and Fraunhoffer diffraction and application to measurement, partially coherent light, diffraction and image formation. Microscopic and macroscopic forms of Maxwell’s equations, energy flow in electromagnetic fields, dipole radiation from Lorentz atoms, partially polarized radiation, spectral line broadening, dispersion, reflection and transmission.

**General Relativity and Cosmology**

Foundations of general relativity, elements of tensor analysis, Schwarzschild and Kerr spacetimes, black hole physics, gravitational radiation, gravitational lensing, cosmological models, observational tests, the early universe, the microwave background, formation of structuresd dark matter and dark energy.

**Physics of Compact Objects**

Physical properties of black holes, white dwarfs, and neutron stars, formation of compact objects, equilibrium configurations, equations of state, stability criteria, and mass limits: the influence of rotation and magnetic fields, pulsar phenomena, black hole spacetimes, Hawking radiation, mass flow in binary systems, spherical and disk accretion, high-temperature radiation processes,pulsar spin-up, compact x-ray sources and x-ray bursts, supermassive black holes in star clusters and galactic nuclei, gravitational and neutrino radiation from supernova collapse and binary coalescence.

**Diffuse Matter in Space**

Discussion of the important physical processes in the interstellar medium, including heating and cooling, atomic and molecular excitation, chemical reactions, ionization and recombination, radiative transfer, fluid dynamics, and physics of interstellar dust. Review of observational evidence from which properties of the interstellar medium are inferred. Problems considered include physical conditions in interstellar clouds, interstellar shock waves, effects of cosmic rays, magnetic fields, and star formation.

**Stellar Atmospheres**

Fundamentals of radiative transfer, radiative flux, specific Intensity and its moments, Radiative pressure, Radiative transfer equation, line and continuum optical depths and source functions, Eddington-Milne approximation, Chandrasekhar solution model atmospheres, equation of state, Saha’s ionization equation, local thermodynamic equilibrium models, convective equilibrium, Non-LTE models, spectral line analysis, photoionisation equilibrium, thermal equilibrium, calculation of absorption and emission line spectra, comparison of theory with observations, calculations of chemical composition, mass-loss/transfer, study of stellar winds, circumstellar envelopes, study of geometry, temperature, and density distribution of the extended atmospheres or ejecta around stellar objects.

**Galactic Structure & Dynamics**

Galactic structure: Local and large scale distribution of stars and interstellar matter, the spiral structure, the Galactic centre, Galactic dynamics, stellar relaxation, dynamical friction, star clusters, density wave theory of galactic spiral structure, chemical evolution in the galaxy, stellar populations, galaxies, morphological classification of galaxies, clusters of galaxies, interactions of galaxies, dark matter, evolution of galaxies.

**Sun & Solar System**

The sun, helioseismology, convection, solar magnetism: flux tubes, sun spots, dynamo, solar cycle, chromosphere, corona, solar wind, physical processes in the solar system; dynamics of the solar system; physics of planetary atmospheres; individual planets; comets, asteroids, and other constituents of the solar system; extra-solar planets; formation of the solar system, stars, and planets.

**Detailed Syllabus for integrated M.Tech-Ph.D programme**

**Mathematical Techniques for Astrophysics**

Vector space and matrices, linear independence, bases dimensionality, Inner product, tensors, transformations of, parallel transport, linear transformation matrices, inverse, orthogonal and unitary matrices, independent element of a matrix, Eigen values and Eigen vectors, diagonalization, complete orthonormal sets to functions, series, convergence tests; complex Variables, Cauchy- Riemann condition, analytic functions, Cauchy’s theorem, Cauchy integral formula, Laurent series, singularities, residue theorem, contour integration, evaluation of definite integrals. Differential equations, second order linear ODEs with variable coefficients, Solution by series expansion, non-homogeneous differential equations and solution by the method of Green’s functions with applications. Eigenvalue methods, up to Strum-Liouville systems. Special functions, Legendre, Bessel, Hermite and Laguerre functions with their physical applications, generating functions, orthogonality conditions, recursion relations, Integral transforms, Fourier integral and transforms, inversion theorem, Fourier transform of derivatives, convolution theorem, Laplace Transform(LT), LT of Derivatives, Inverse LT, Fourier series; properties and applications, discrete Fourier transform.

**Electromagnetics and Wave Optics**

Maxwell equation of electromagnetic waves, Propagation through free space, Guided wave and waveguides, Hertzian dipole radiation antenna, Dipole antennas as receiving antenna, Reflection antenna, Radiation pattern analysis, Cassegrainian antenna, Synthetic aperture antenna, Propagation of E.M. wave through plasma, Light as E.M.Wave, Huygen – Fresnel principle for light propagation, geometrical theory of propagation of light, Eikonal equation for propagation of light in homogeneous and inhomogeneous media.

**Astrophysical Concepts**

Astronomy fundamentals, Black body radiation, Radiation mechanism, Flux density and luminosity, basics of Radiative transfer and Radiative processes, Magnitudes, Motions and Distances of Stars : Absolute stellar magnitude and distance modulus, Bolometric and radiometric magnitudes, Colour-index and luminosities of stars, Stellar positions and motions, Velocity dispersion, Statistical and moving cluster parallax, Extinction, Stellar temperature, Effective temperature, Brightness temperature, Color temperature, Kinetic temperature, Excitation temperature, Ionization temperature, Spectral Classification of stars, Utility of stellar spectrum, stellar atmospheres.

Overview of the major contents of the universe, Sun and stars, stellar interiors, HR diagram, nuclear energy generation, neutrino astronomy, white dwarfs and neutron stars, plasma processes, compact objects, shape, size and contents of our galaxy, basics of stellar dynamics, normal and active galaxies, gravitational wave astronomy, high energy physics, Newtonian cosmology, microwave background, early universe.

**Optical Techniques in Astrophysics**

Coherence : Physical origin of line widths, Temporal and spatial coherence, Coherent scattering and dispersion, Propagation of mutual coherence, Degree of coherence, Van Cittart-Zernike theorem, Application of coherence theory to astronomy.

Diffraction: Occurrence of diffraction, Scalar wave approximation, Kirchoff’s scalar diffraction theory, Fresnel diffraction, Frounhoffer diffraction and Fourier optics.

Polarization: Nature of polarized light, Dichorism, Birefringence, Scattering and polarization, Polarizing devices, Mueller matrix, Jones matrix formalism.

Ray-Optical theory of image formation: Paraxial approximation, Optical invariants, Doppler shift and its consequence

Aberration measure : Ray and wave aberrations – interrelationship – reference sphere, Power series expansion for axially symmetric systems, Aberration types and orders, Zernike circle polynomials, Chromatic aberration, Secondary spectrum

Diffraction theory of image formation : Airy pattern, Two-point resolution, Rayleigh criterion of resolution, Point spread function of aberrated system, Aberration tolerances, Marechal criterion, Aberration balancing, System theoretic viewpoint of image formation, principles of superposition, Space invariance and isoplanatism, Optical transfer function, Modulation transfer function, Phase transfer function, Factor of encircled energy, Strehl ratio, Merit function.

**Observational Techniques in Astronomy**

Telescopes at different wavelengths, imaging, spectroscopy, Spectro-polarimetry.

Theory of atmospheric turbulence, Basic formulations of atmospheric turbulence, Turbulent flows, Inertial subrange, Structure functions of the velocity field, Kolmogorov spectrum of the velocity field, Statistics of temperature fluctuations, Refractive index fluctuations, Experimental validation of structure constants, Imaging in randomly inhomogeneous media Seeing-limited images, Atmospheric coherence length, Atmospheric coherence, Aniso-planatism.

Speckle : Origin of speckle, Random phasor sums, First-order statistics of intensity and phase, Sum of speckles, Multidimensional statistics of speckle, Electronic speckle pattern interferometry (ESPI), Autocorrelation function and power spectrum of speckle, Speckle in imaging through atmosphere, Astronomical speckle interferometry, Cross-spectrum technique, Bispectrum technique.

Optical aperture synthesis: single aperture and multiaperture synthesis, phase closure techniques, resolving power of an interferometer, Nulling interferometry, Baseline geometry, (u, v) – plane tracks, Beam combination, Delay-lines, Phase and group delay tracking, Calibration, Limitations and constraints of interferometry, visibility determination, Data Processing: Aperture synthesis mapping.

**Detection Techniques in Astronomy**

Stellar interferometry: Fizeau-Stephan interferometer, Michelson stellar interferometer

Radio interferometry: Radio telescope, Brightness and antenna temperatures, Sensitivity, Brightness distribution, Radio interferometer, Fringe visibility, Very long baseline interferometry, Intensity interferometry: Intensity interferometer in radio and visible wavelengths, Narrabri intensity interferometer, Intensity correlations in partially coherent fields, Correlation between the signals of the photo-detectors.

Detectors, Photo-electric effect, Detecting light, Photo-detector elements, Detection of photo-electrons, Photo-multiplier tube, Image intensifiers, Single photon counter, sensitivity, noise, quantum efficiency, spectral response, Johnson noise, signal to noise ratio, background, aberrations, detectors at different wavelengths, calibration, CCD, CMOS, Correlation measurements.

**Control Instrumentation & Adaptive Optics**

Digital signal and digital signal processor (DSP); Programmable logic controller (PLC), Field programmable gate array (FPGA), Embedded system PID controller, Direct digital controller, Distributed controller, supervisory controller optimum controller, adaptive controller: model reference and self tuning controller. Adaptive Optics, Basic principles, Elements of adaptive optics systems, Wavefront sensors, Wavefront reconstruction, Reference source, Multi-conjugate adaptive optics

**Computational Astrophysics, Statistics and Data Mining**

Coordinate systems, precession, time, heliocentric corrections; methods of observation, resolution, methods of data reduction, Fourier transforms, calibrations; Numerical techniques, errors and error propagation, numerical integration and interpolation, random numbers, astrostatistics, probability distributions, hypothesis testing, sampling methods, multivariate analysis, regression, time-series analysis, data reduction, error analysis, numerical solutions of algebraic, ordinary differential and partial differential equations.

**Detailed Syllabus for Ph.D programme**

**Courses offered during August Term (First Semester)**

**Radiative Processes in Astrophysics**

Elements of radiative transfer and stellar atmospheres. Theory of grey atmospheres. Covariant formulation of classical electrodynamics. Radiation from accelerated charges. Cyclotron and synchrotron radiation. Bremsstrahlung. Thomson and Compton scattering. Plasma effects. Atomic and molecular spectra. Transition rates and selection rules. Opacity calculations. Line formation in stellar atmospheres

**Introduction to Fluid Mechanics and Plasma Physics**

Boltzmann equation. Derivation of fluid equations. An introduction to stellar dynamics. Important properties of ideal and viscous fluid flows. Gas dynamics. Waves in fluids. Hydrodynamics stability. Turbulence. Plasma orbit theory. Debye shielding and collective behaviour. Waves and oscillations in plasmas. From the Vlasov equation to MHD equations. Flux freezing. MHD waves. Reconnection and relaxation. Dynamo theory.

**Astronomical Techniques**

Radio: coordinate system, detection principles, resolution and sensitivity, interferometry and aperture synthesis. IR/Optical/UV: CCD fundamentals, imaging systems, point-spread-function, sensitivity, photometry and spectroscopy, speckle techniques, adaptive optics. X-ray/Gamma-ray astrophysics: detection principles, detectors and imaging systems, resolution and sensitivity, detector response, data analysis methods for spectroscopic and timing studies. Coordinated laboratory / data analysis exercises in each of the three areas.

**Stellar Structure and Evolution**

Introduction to stellar photometry, stellar spectra, HR diagram, Equations of Stellar Structure, Polytropes: Lane Emden equation and its solution, Energy Generation in Stars: Calculation of thermonuclear reaction rates for non-resonant and beta-decay reactions; The various reaction chains: pp-I,II,III, CNO, He-burning, C-burning, Si-burning, photo-dissociation, Neutrino emission from Stars: Solar neutrinos, neutrinos from supernovae, terrestrial detection of stellar neutrinos, stellar degeneracy and equations of state (EOS): EOS for non-degenerate and degenerate matter, Equation of state for matter at near-nuclear and nuclear densities, Final stages of stellar evolution: Supernovae (a basic understanding of the core-collapse process and the structure of the progenitor) and neutron stars (a basic knowledge of NS structure, the problems associated with determining a unique equation of state for NS).

**Courses offered during January Term (Second Semester)**

**Galaxies and Interstellar Medium**

Galactic structure: local and large scale distribution of stars and interstellar matter, the spiral structure, the galactic centre. Galactic dynamics, stellar relaxation, dynamical friction, star clusters, density wave theory of galactic spiral structure, chemical evolution in the galaxy, stellar populations. Galaxies, morphological classification of galaxies, active galaxies, clusters of galaxies, interactions of galaxies, dark matter, evolution of galaxies.

**Stellar and High Energy Astrophysics**

Stellar structure. Stellar evolution. Nuclear astrophysics. Supernovae. White dwarfs. Neutron stars. Black holes. Binary stars. Pulsars. Accretion physics. X-ray and gamma ray astronomy. Neutrino astrophysics.

**Numerical and Statistical Techniques**

Numerical techniques in physics and astrophysics: numerical integration and interpolation. Numerical solutions of algebraic, ordinary differential and partial differential equations. Random numbers. Statistics techniques: probability, discrete and continuous random variables, central limit theorem, random walk and Poisson processes. Hypothesis testing, sampling methods, multivariate analysis, regression, time series analysis, Fourier transforms. Data reduction, error analysis. techniques.

**General Relativity and Cosmology**

Foundations of general relativity. Elements of tensor analysis. Schwarzschild and Kerr spacetimes. Black hole physics. Gravitational radiation. Cosmological models. Observational tests. The early universe. The microwave background. Formation of structures.