Introduction to materials and techniques; Spectroscopic methods- UV-visible and vibrational spectroscopy- Infrared and Raman, Electron spectroscopies - X-ray photoelectron spectroscopy, Ultra-violet photoelectron spectroscopy, Auger electron spectroscopy; Optical microscopy, Electron microscopy- SEM, TEM; Scanning Probe Microscopies: STM, AFM; Thermal analysis- TGA, DTA, DSC; Materials analysis by Non-destructive testing (NDT).

Detailed version

Introduction: General instrumental parameters, measurement basics.

Mathematical concepts; Introduction to solution techniques for ordinary differential equations,  Sturm-Liouville problems, Partial differential equations, Applications of PDE in heat transfer, mass transfer, diffusion, fluid flow, chemical reaction, transport process and process modeling-simulation, Boundary layer concept, balance equations for mass, momentum, energy; and estimation, Heat Transfer; Governing equations and boundary conditions; conduction, convection and radiation; Balance equations for mass transfer, Ideal reactors, Modeling of ideal reactors, solution techniques for mo

Introduction- Size and shape dependent properties and their uniqueness; surface characteristics and stabilization; Quantum confinement; Zero dimensional, one dimensional and two dimensional nanostructures - Processing of  nanomaterials - down and bottom up approaches-metal nanoparticles, quantum dots, nanoclusters, carbon based nanomaterials, core-shells, organic, inorganic, hybrid nanomaterials, biomimetic nanomaterials. – Techniques for characterization and property evaluation- relevant applications- societal implications and risk factors

Structure of solids,  Significance of structure property relationship; Diffusion phenomenon, Applications of diffusion; Principles of solidification, Phase diagrams and phase transformations, Heat treatment; Ceramic materials, Classification, Synthesis, Properties, Characterization and applications

Detailed version

Characteristics of the Sun – internal structure – s olar observations – solar atmosphere – oscillations – Convection – rotation – magnetism – chromosphere – corona – solar wind – quiet Sun – Active Sun – Helioseismology

Properties of known exoplanets – exoplanet surveys – detection methods – formation, interior and evolution of planets – brown dwarf exoplanets c onnection – close orbiting exoplanets – multiple planet systems – planets in binary systems – moons of exoplanets Origin of life – prebiotic molecules and developmen t of life forms – habitable zone – Mars and life – Icy bodies (Europa and others) – Titan’s atm osphere – detection of exoplanets – search for extraterrestrial life.

Scientific background : Variable stars, binary star s and their evolution, supernovae, pulsars and associated phenomena (even include testing theories of gravity using pulsars), accretion and associated phenomena (like x-ray bursts), gamma-ray bursts, rotating radio transients (RRATS), jets & outflows (micro-quasars etc), AGNs-blazars-Q SOs A survey of missions and their ways of operation [c an go to technical levels, to the operations of these instruments] :- Optical/IR surveys : Pan-STAR RS (Panoramic Survey Telescope and Rapid Response System), PTF (Palomar Transient Fact ory), Trans

Atomic structure: review of Schrodinger equation - overview of single and multiple electron systems - perturbations and level splittings - pari ty - spin orbit coupling - zeeman effect - hyperfine structure - Boltzmann population of energ y levels in thermal equilibrium - Saha equation. Radiative transitions: semi-classical the ory - dipole approximation - Einstein coefficients and oscillator strengths - selection r ules and transition rates.

Unpolarised light, Linear, Circular, Elliptical pol arised light, Partially and fully polarised light, Stokes parameters, Dichroism, Birefringence, Poinca re sphere - Mueller and Jones representations with applications - Complex plane o f polarisation states. Generation of polarised light in astronomy - polari sation by reflection, scattering geometry, magnetic fields - dependence on refractive index - synchrotron emission - Faraday rotation - Dust in ISM.

Basic cosmology - Expansion of the universe -- scal e factor -- cosmological redshift -- descriptive overview of inflation, unification of f orces and fundamental particles. Primordial nucleosynthesis -- elemental abundances : predictio ns and observations. Cosmic Microwave Background - detection, power spectrum, origin of C MB, anisotropies in the CMB and their origin -- overview of COBE and WMAP probes - missio n and instrumentation.