Module Information

Module Identifier
Module Title
Advanced Numerical Methods
Academic Year
Semester 1
External Examiners
  • Professor Pete Vukusic (Professor - Exeter University)
Other Staff

Course Delivery

Delivery Type Delivery length / details
Lecture 11 x 1 Hour Lectures
Practical 11 x 2 Hour Practicals


Assessment Type Assessment length / details Proportion
Semester Assessment Continuous assessment of coursework.  50%
Semester Assessment A numerical project report.  50%
Supplementary Assessment As determined by the Departmental Exam Board  100%

Learning Outcomes

On successful completion of this module students should be able to:

Demonstrate a familiarity with various techniques and algorithms for scientific computing and analysis.

Devise and implement numerical programs to perform the relevant algorithms.


Numerical solutions to mathematical and physics problems is a cornerstone of both physics and applied mathematics research. This module is a continuation of the practical-based module PH36010. The numerical techniques are more advanced and will require more detailed understanding of the numerical methods.

Brief description

This module builds on the Numerical Methods module PH36010. Methods of solving (large) systems of simultaneous linear equations are introduced. This is then used to numerically solve partial differential equations. Monte Carlo methods are introduced as a general method. More specifically, Metropolis Monte Carlo methods for solving problems in statistical mechanics are covered. The students will implement these algorithms and apply them to simple physical problems.


LU decomposition.
Iterative methods for solving sparse systems of linear equations.
Numerical methods for partial differential equations.
Monte Carlo methods.
Metropolis Monte Carlo methods for simulation of statistical mechanical systems.

Module Skills

Skills Type Skills details
Application of Number Throughout the module.
Communication Writing reports.
Information Technology This module involves programming and computational visualisation.
Personal Development and Career planning Programming skills.
Problem solving Throughout the module.
Subject Specific Skills Programming, numerical methods.


This module is at CQFW Level 7