1. An essential introduction to a programming language [20 Hours]
Introduction to any one of the programming language in Fortran/C/C++/Python.
2. Root-finding and numerical integration [20 Hours]
Root-finding methods: bisection method, Newton’s method, Newton’s method and shooting, steepest descent. Basic integration schemes, stochastic methods for multi-dimensional integrals.
3. Numerical solutions of differential equations [ 20 Hours]
The Verlet method, Runge–Kutta methods, classical equation of motion, systems with chaotic dynamics.
4. Monte-Carlo simulations and Molecular Dynamics in statistical mechanics [32 Hours]
The Metropolis algorithm for equilibrium statistical mechanics, studies of the phase transition in the Ising model of magnetism, cluster algorithms, molecular dynamics.
5. Numerical solutions of quantum mechanical problems [28 Hours]
Eigenstates of the Schrodinger equation, time-evolution of wave-packets, quantum spin systems (ground state and finite-temperature properties).
References
Michael Metcalf, John Reid, and Malcolm Cohen, Modern Fortran Explained: Incorporating Fortran 2018, Oxford University Press.
Bjarne Stroustrup, The C++ Programming Language (4th Edition), Addison-Wesley.
John M. Stewart, Python for Scientists (2nd Edition), Cambridge University Press
W. H. Press and S. A. Teukolsky, Numerical Recipes (3rd Edition), Cambridge University Press.
Werner Krauth, Statistical Mechanics: Algorithms and Computations, Oxford University Press.
J. M. Thijssen, Computational Physics (2nd Edition), Cambridge University Press.
Joel Franklin, Computational Methods for Physics, Cambridge University Press.
N. J. Giordano and H. Nakanishi, Computational Physics (2nd Edition), Addison-Wesley.
R. H. Landau et al., Computational Physics: Problem Solving with Computers, Wiley-VCH.
D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (4th edition), Cambridge University Press.
Examinations