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Module MA5633A: Numerical Methods
 Credit weighting (ECTS)
 5 credits
 Semester/term taught

First Semester 201617
 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, LUdecomposition, norms and errors, condition numbers, iterations, perturbation analysis. Iterative methods, Jacobi, GaussSeidel, nonstationary methods, Sparse matrix solvers.
 Numerical solution of ordinary differential equations: Euler's method, RungeKutta method, multistep methods, predictorcorrector methods, rates of convergence, global errors, computer implementation. Methods for stiff differential equations.
 Assessment Detail
 80% twohour written examination. 20% continuously assessed assignments throughout the semester.