2008/09 Undergraduate Module Catalogue

MATH2600 Numerical Analysis

10 creditsClass Size: 200

Module manager: Dr E. Kersale
Email: kersale@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

Pre-requisite qualifications

(MATH1932 or MATH1960) and (MATH1015 or MATH1331), or equivalent.

This module is approved as an Elective

Module summary

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).

Objectives

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

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

Delivery type	Number	Length hours	Student hours
Example Class	11	1.00	11.00
Lecture	22	1.00	22.00
Private study hours			67.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			100.00

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 16/07/2010

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