EM2060 Numerical Methods

Preliminaries: Floating point arithmetic, Big O notation, matrix norms, Review of programming Error Analysis: Numerical solutions to nonlinear equations: Fixed point iteration, Bisection method, Newton-Raphson method Numerical solutions to systems of linear equations: Gaussian elimination, Jacobi method, Gauss-Seidel method Interpolation: Lagrange interpolating polynomial, Newton’s interpolating polynomials, Spline interpolation Numerical integration: Trapezoidal rule, Simpson rule, Gaussian quadrature Numerical solutions to ordinary differential equations: Initial value problems: Euler method, Runge - Kutta methods; Boundary value problem: Finite difference method, Adaptive step size mechanisms Numerical solutions to partial differential equations: Explicit and implicit finite difference methods, Basics of finite element methods Computational labs: Covering selected topics & appropriate problems from the respective fields