Faculty of Science

Objectives

To get acquainted with numerical methods for solving linear and non-linear physical problems, as well as problems related to strongly correlated electron systems.

Contents

Errors: its sources, propagation and analysis, computer representation of numbers; Roots of non-linear equation: Bisection, Newton-Raphson, Secant methods; System of non-linear equations, Newton’s methods for non-linear equations; Applications in Physics problems; Solutions of linear systems: Gauss, Gauss-Jordan elimination, matrix inversion and LU decomposition; Eigenvalues and eigenvectors, applications; Interpolations and curve fittings: introduction to interpolation, Lagrange approximation, Newton and Chebyshev polynomials; Least square fitting, linear and non-linear, applications; Numerical differentiation and integration: approximating the derivative, numerical differentiation formulas, introduction to quadrature, trapezoidal and Simpson’s rules, Gauss-Legendre integration, applications; Solutions of ODE: initial value and boundary value problems, Euler’s and Runge-Kutta methods, finite difference methods; Solutions of PDE: hyperbolic and elliptic equations by finite difference; Applications to 2D equations; Stochastic methods, Molecular dynamics, Monte-Carlo methods: Importance sampling, Metropolis algorithm, data analysis, finite-size effects, data samplings, discrete Fourier transform, FFT, wavelet transforms