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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.

Essential techniques: Probability distributions and statiscs, error analysis and error propagation, covariance, least-square fitting. Vacuum technology: gas flow equations, flow regimes, types of pumps, gauges and seals. Sensors and analog instrumentation: analog signal processing. Lock in amplifiers and applications: measurements in noise prone environments. Digital electronics: microprocessors and micro-controllers, ADC/DAC, PLCs, computer interfaces.

Semiconductor in equilibrium: Equilibrium distribution of electrons and holes, qualitative description of dopant atoms and energy levels, equilibrium distribution of electrons and holes in extrinsic semiconductor, degenerate and non-degenerate semiconductors, statistics of donors and acceptors, probability function, compensated semiconductors, Fermi energy levels and its variation with doping concentration and temperature, relevance of Fermi energy.

Approximation methods: Variational methods, WKB approximation; time-indepdndent perturbation theory; time-dependent perturbation theory: Interaction picture, Fermi's golden rule, sudden and adiabatic approximations.

Scattering theory: Transition rates and cross sections, Lippmann-Schwinger equation, scattering amplitude, Green's functions; Born approximation; phase shifts and partial waves.