Program Overview

Numerical Methods (MATH0033)

Key Information

• Faculty: Faculty of Mathematical and Physical Sciences
• Teaching department: Mathematics
• Credit value: 15
• Restrictions: This module is normally taken (at level 6 UG) by third year students on single or combined honours mathematics degrees or (at level 7 PG) by students on the MSc in Mathematics or on the MSc in Scientific Computing Physics and Astronomy. It may be suitable for other students with some programming experience and a strong mathematical background, including some analysis, algebra and mathematical methods (as covered by mathematics students in MATH0004/MATH0006/MATH0011).

Alternative Credit Options

There are no alternative credit options available for this module.

Description

Many phenomena arising in engineering and the physical and biological sciences can be described using mathematical models. Frequently the resulting equations can not be solved analytically, in which case a common approach is to use a numerical method to find an approximate solution. The aim of this course is to give an introduction to the ideas underpinning computational mathematics and then introduce a series of methods to solve different problems. The overarching goal is to provide the fundamental tools for the solution of large scale differential equations. Indeed such problems require the understanding of several subproblems and in this course we introduce the most important building blocks: solution methods for nonlinear equations and systems, solution methods for large linear systems and methods for ordinary differential equations. For each method we typically ask two questions: 1. Under what circumstances is the numerical solution a good approximation of the true solution? 2. How much better does the approximation become if we are able to devote more computational resources to its calculation? To answer these questions we will draw on tools from analysis including the mean value theorem, Taylor's theorem and the contraction mapping theorem. The homework consists of theoretical problems where different properties of the methods are explored and a numerical part that serves as a hands on illustration of the theoretical material. The last computational exercise is slightly more challenging, putting together several of the elements in the course for the solution of an initial boundary value problem. These numerical exercises are designed to be solved using MATLAB and several MATLAB scripts are distributed during the course. However any programming language may be used depending on the experience and interest of the student.

Module Deliveries for 2026/27 Academic Year

Intended Teaching Term: Term 1, Postgraduate (FHEQ Level 6)

Teaching and Assessment

• Mode of study: In person
• Methods of assessment:
  • 80% Exam
  • 20% Coursework
• Mark scheme: Numeric Marks

Other Information

• Number of students on module in previous year: 10
• Module leader: Professor Iain Smears

Intended Teaching Term: Term 1, Undergraduate (FHEQ Level 6)

Teaching and Assessment

• Mode of study: In person
• Methods of assessment:
  • 80% Exam
  • 20% Coursework
• Mark scheme: Numeric Marks

Other Information

• Number of students on module in previous year: 99
• Module leader: Professor Iain Smears