Ordinary differential equations: methods for numerical integration: multistep algorithms and implicit algorithms.

 

Classical molecular dynamics: Verlet algorithm, predictor-corrector algorithms, determination of macroscopic parameters, Nosé-Hoover thermostat, constraints, Ewald summations, application to Lennard-Jones liquids.

 

Random variables: definitions and properties, generators and distribution functions, central-limit theorem.

 

Random walks: binomial and Gaussian distributions, particle diffusion, Brownian motion.

 

Monte Carlo integration: direct sampling, importance sampling, Metropolis algorithm, errors in correlated sampling, Monte-Carlo simulations of Lennard-Jones liquids and of two-dimensional spin systems.