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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. This includes an introduction, beginners tutorials and exercises in these softwares as well as and X-ray data analysis.

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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.

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

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.

Solid state NMR studies in condensed matter liquid-crystalline materials: The liquid-crystalline state, orientational order phase symmetry, molecular orientational order, the general time-independent NMR Hamiltonian for liquid crystalline samples, molecular order parameters, different representations of the order parameters, molecular order parameters and the symmetry of rigid molecules, director alignment, dipolar couplings between nuclei in rigid molecules in liquid-crystallline phases, deuterium quadrupolar splittings for rigid molecules in liquid-crystalline phases, che

Theory of solid state NMR and its experiments: The basics of solid state NMR, the vector model of pulsed NMR, the quantum mechanical picture: Hamiltonians and the Schrodinger equation, the density matrix representation and coherences nuclear spin interactions, calculating NMR power patterns, general features of NMR experiments.

Nuclear spin interactions in solids: Basic nuclear spin interactions in solids, spin interactions in high magnetic fields, transformation properties of spin interactions in real space, powder spectrum ilne shapes, specimen rotation, rapid anisotropic molecular rotation, ine shapes in the presence of molecular reorientation.

Elements of Resonance: Introduction, Simple resonance theory, Absorption of energy and spin-lattice relaxation. Basic theory: Motion of isolated spins – Classical treatment, Quantum mechanical description of spin in a static field, Equations of motion of the expectation value, Effect of Alternating Magnetic Fields, Exponential Operators, Quantum mechanical treatment of a rotting magnetic field, Bloch equations, Solution of the Bloch equations for low H1, Spin Echoes, Quantum mechanical treatment of the spin echo.

Atomic gases, Collisions and trapping, Interaction with the radiation filed and optical traps, Light forces on atoms, Doppler and sub-Doppler cooling, Magneto-Optical Trap, evaporate cooling, Optical Lattices, Ion traps , experiments on cold atoms. The Ideal Bose gas, Weakly-interacting Bose gas, Ground state energy and equation of state, Particles and elementary excitations. Nonuniform Bose gases at zero temperature, Gross-Pitaevskii equation , Thomas-Fermi limit, solitons, quantization and elementary excitations.