## MATH2600 Numerical Analysis

### 10 creditsClass Size: 200

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2005/06

### Pre-requisites

(MATH1921 or MATH1931) and (MATH1011 or MATH1330), or equivalent.

This module is approved as an Elective

### Objectives

a) To show how to tackle by numerical methods many fundamental mathematical problems that cannot be solved by analytical means.. On completion of this module, students should be able to:. describe how errors arise in computations;. solve simple non-linear equations by root-finding techniques;. calculate the interpolating polynomial through discrete data points;. derive and use quadrature formulae based on integration of polynomial interpolates;. write down suitable numerical schemes for solving first order ordinary differential equations;. solve linear systems of algebraic equations using Gaussian elimination and LU factorisation.

### Syllabus

Most of the problems that students meet when they are introduced to, for example, integration or differential equations, will have nice analytic solutions. In real life though this is typically not the case and so solutions have to be evaluated numerically (i.e. with the aid of a computer). This module explains how to express mathematical operations in terms of operations that can be performed on a computer. It is a good preparation for the Level 3 module in Numerical Methods (MATH 3473)

The topics covered are: 1. Introduction. Computer arithmetic. Errors; round-off error, truncation error.. 2. Solution of nonlinear equations in one variable. Bisection method; fixed point iteration; Newton-Raphson iteration; secant method. Order of convergence.. 3.Interpolation. Lagrange interpolation; error term. cubic splines.. 4.Numerical integration. Trapezoidal rule. Method of undetermined coefficients. Simpson?s rule. Newton-Cotes formulae. Composite integration methods. Richardson extrapolation; Romberg integration.. 5.Ordinary differential equations (initial value problems). Euler?s method; errors. Runge-Kutta methods. Multi-step methods. Stability.. 6.Linear systems of algebraic equations. Gaussian elimination. Pivoting. LU factorisation.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures (22 hours) and examples classes (11 hours).

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

2 hour written examination at end of semester (100%).