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Module MA5633A: Numerical Methods

Credit weighting (ECTS)
5 credits
Semester/term taught
First Semester 2016-17
Module Coordinator
Marina Marinkovic
Intended Learning Outcomes
Students who successfully complete the course should be able to:
  • Use numerical methods to solve systems of linear equations and some examples of nonlinear equations.
  • Describe how to solve optimisation problems numerically.
  • Construct numerical solutions to simple differential equations.
  • Analyse a mathematical problem and determine an appropriate numerical technique to solve it and describe logically how to code it in algorithmic form.
  • Use Matlab, its instructions and its programming language.
 
Structure and Content
MATLAB programming: data types and structures, arithmetic operations, functions, input and output, interface programming, graphics, implementation of numerical methods.
Finite floating point arithmetic: catastrophic cancellation, chopping and rounding errors.
Data handling and function approximation: curve fitting using regression and splines, Discrete Fourier Transform.
Solution of nonlinear equations: bisection method, secant method, Newton's method, fixed point iteration, Inverse Quadratic Interpolation, polyalgorithms.
Numerical optimization: Newton's method, steepest descents.
Solutions of linear algebraic equations: Matrix factorisation, forwarding, Gaussian elimination, pivoting, scaling, back substitution, LU-decomposition, norms and errors, condition numbers, iterations, perturbation analysis. Iterative methods, Jacobi, Gauss-Seidel, non-stationary methods, Sparse matrix solvers.
Numerical solution of ordinary differential equations: Euler's method, Runge-Kutta method, multi-step methods, predictor-corrector methods, rates of convergence, global errors, computer implementation. Methods for stiff differential equations.
Assessment Detail
80% two-hour written examination. 20% continuously assessed assignments throughout the semester.