The course aims for a somewhat rigorous exposition to numerical methods useful in solving a variety of problems that appear in modern Physics research. The idea is to enable students to make careful and deliberate use of computational methods for their research in physics and astronomy.
- Numerical differentiation and integration: Finite differencing, convergence, error estimates, Richardson extrapolation, trapezoidal rule, Romberg's method, Simpson's rule, Gaussian quadrature.
- Ordinary differential equations: Euler methods, Runge-Kutta methods, Adaptive step size control.
- Partial differential equations: Stability analysis, well-posedness, Finite difference and spectral methods, Solving Hyperbolic, Elliptic and Parabolic PDEs.
- Fourier methods and signal processing: Fast Fourier transform, sampling theorem, windowing, convolution and correlation, power spectrum estimation, Matched filtering.
- Monte-Carlo methods and statistical techniques: Markov-chain Monte Carlo methods, Metropolis–Hastings algorithm, Bayesian inference, Hypothesis testing, Model selection.
- Algebraic Equations and root finding: Solving systems of linear equations, non-linear root finding.