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

Overview of Solar system - Dynamics: Two-body problem, Three-Body Problem (Lagrangian points) - Resonances - Tidal forces - Solar energy balance and transport: Radiative Equilibrium - Planetary Atmospheres: Structure, Composition, Atmospheric Escape - Planetary surfaces: Surface morphology - Impact cratering - Minor Bodies: Meteories, Asteroids, Comets, Minor planets, Trans-Neptunian Objects, Centaurs - Planetary rings - Planet formation: Evolution of protoplanetary disks, Growth of solid bodies, Formation of Terrestrial and Giant planets - Planetary Migration: - Extrasolar Planets: Detecti

Sky coordinates and motions: Earth Rotation - Sky c oordinates - seasons - phases of the Moon - the Moon's orbit and eclipses - timekeeping (side real vs synodic period); Planetary motions - Kepler's Laws - Gravity; Light & Energy - Telescope s - Optics - Detectors; Planets: Formation of Solar System - planet types - planet atmospheres - extrasolar planets; Stars: Measuring stellar characteristics (temperature, distance, luminosity, mass, size) - HR diagram - stellar structure (equilibrium, nuclear reactions, energy transport) - stellar evolution; Galaxies: Our Milky Way - Galactic stru

Tutorials on Fitting techniques (linear and non-linear, fits to data with experimental errors, evaluating goodness of fit, etc) and error analysis , Handling of data and getting familiar with data analysis packages like IRAF, AIPS and CASA. Th is includes an introduction, beginners tutorials and exercises in these softwares as well as and X-ray data analysis

Overview of numerical computation - Simple problems: data sorting, root finding etc. - Numerical solutions of algebraic equations - Numerical integration, interpolation/extrapolation - Numerical differentiation - Ordinary differential equations - Partial differential equations - Statistics, Least-squares fitting - Data crunching, dealing large data set - Fourier transform - Advanced Applications in Astrophysics: N-Body Methods, Hydrodynamics - Monte Carlo Methods

Concepts of Radiative Transfer – special relativity – Maxwell’s equations – Wave equation – retarded potentials – radiation field – Poynting vector – radiation from accelerated charge – bremsstrahlung – Thomson and Compton scattering – synchrotron radiation – thermal and non-thermal distribution of radiating particles – non-thermal synchrotron radiation – self-absorption – synchrotron and Compton cooling – Inverse Compton catastrophe and brightness temperature limit – propagation effects: dispersion, faraday rotation, depolarization – Atomic and molecular spectra – fine structure and hyperf

Telescopes and Detectors – optical, infrared, radio, x-rays, gamma-rays, neutrinos and cosmic rays; Gravitational radiation; Detection of dark matter and Dark Energy Astronomy from Space;Imaging – focal plane imagers, PSF and deconvolution, interferometry Photometry, Spectroscopy, Polarimetry, Astrometry; Solar telescopes; Surveys, Astronomical databases, Virtual Observatory

Basic concepts, composition of the atmosphere, equation of state, hydrostatic equilibrium, first law of thermodynamics, application of first law, entropy, second law, heat capacity, dry adiabatic processes, transfer processes, moist thermodynamic processes in atmosphere, static stability, cloud characteristics and processes, Global energy and entropy balances, thermodynamic feedback in the climate system, thermodynamic diagrams.