Module Information

Module Identifier
Module Title
Advanced Numerical Methods
Academic Year
Semester 1
Second and third year physics
Other Staff

Course Delivery

Delivery Type Delivery length / details
Lecture 10 x 1 hour lecture
Practical 12 x 2 hour workshops


Assessment Type Assessment length / details Proportion
Semester Assessment Exercises set in semester week 8 comprising a portfolio drawn from coursework.  40%
Semester Assessment Mini project set in semester week 8 for Completion by the end of term.  60%
Supplementary Assessment Resubmit failed components  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. There will also be an introduction to parallel programming using the MPI library.


LU decomposition.
Iterative methods for solving sparse systems of linear equations.
Numerical methods for partial differential equations.
Introduction to parallel programming using the Message Passing Interface.
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 a portfolio.
Information Technology Python, Fortran, MPI.
Personal Development and Career planning Programming skills.
Problem solving Through the module.
Subject Specific Skills Programming, numerical methods.


This module is at CQFW Level 7