Computational Methods in Physics

The module presents basic computational methods useful for physics and science students. The lectures cover: (1) Basic numerical methods - differentiation, integration, interpolation, root-finding and random number generators, (2) Differential equations - finite difference method, shooting method and relaxation method; applications to chaotic dynamics of a driven pendulum, one-dimensional Schrödinger equation, and fast Fourier transform, (3) Matrices - Gaussian elimination scheme for a system of linear equations, eigenvalues of Hermitian matrices; Hartree-Fock approximation, (4) Monte Carlo simulations - sampling and integration; random walk and simulation of diffusion equation, stochastic differential equation, Brownian dynamics; variational Monte Carlo simulation; Metropolis algorithm and Ising model, and (5) Finite element methods - basic concepts; applications to the Poisson equation in electrostatics.

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