PHY3028 : Computational Modelling

Semester 2 Credit Value: 10
ECTS Credits: 5.0


To introduce the implementation of mathematical algorithms within practical computer programs. Students will learn the fundamental programming structures, and their implementation in a widely-used programming language: Fortran. Additionally, to introduce numerical and computational modelling techniques in a number of different mathematical topics. Students will be able to interpret such methods algorithmically, and implement them within practical, problem-solving programs.

Module Summary:
Numerical and computational methods are an important part of modern scientific practice, used in almost all branches of mathematics, statistics and physics, and in other fields. These methods are implemented in practice via computer programs, so this module introduces programming as a tool for the implementation of such methods. The emphasis is on the fundamental algorithms and structures, although the material is developed using one specific modern programming languages, to which the students will be introduced: Fortran 95.

The emphasis is on learning in a practical context; we will be writing simple programs from the outset, rather than abstractly studying the language syntax or implementation. The programming will be illustrated and developed through their use in applications from a range of mathematical topics. The algorithmic nature of all the methods covered will be emphasised, highlighting the basic logical structures required.

Outline Of Syllabus

Introduction to programming:
Basic program structure and implementation (editing, compiling, executing); simple data types (integer, real, complex, logical, and character); arrays of data; input and output; branching structures ('if' constructs); repeating structures ('do' loops); program blocks (subroutines, functions, modules, interfaces).

Mathematical applications:
Three mathematical topics will be explored in more detail. For each of these, computational methods will be motivated, and practical algorithms derived and converted into programs. The topics may include: numerical integration; numerical solutions of ODEs and PDEs; linear algebra.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture101:0010:00Formal lectures
Guided Independent StudyAssessment preparation and completion213:0026:00Projects
Guided Independent StudyAssessment preparation and completion25:0010:00Revision for PC examinations
Guided Independent StudyAssessment preparation and completion21:002:00PC Examinations
Guided Independent StudyAssessment preparation and completion18:008:00Written assignment preparation
Scheduled Learning And Teaching ActivitiesPractical181:0018:00Computer practicals
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study14:004:00Assignment and project review
Guided Independent StudyIndependent study120:0020:00Studying, practising and gaining understanding of course material
Jointly Taught With
Code Title
MAS3807Computational Modelling
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Practicals are used to help the students to develop their programming skills but also afford an opportunity to develop the students’ abilities at applying the theory to solving problems. Office hours provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exam Pairings
Module Code Module Title Semester Comment
MAS3807Computational Modelling2N/A
Other Assessment
Description Semester When Set Percentage Comment
Written exercise2M20project work
Written exercise2M20project work
Prob solv exercises2M10One coursework assignment
Computer assessment2M25PC test 1 (60 mins, in-class)
Computer assessment2M25PC test 2 (60 mins, in-class)
Assessment Rationale And Relationship

The project work and coursework assignment allow the students to develop their problem solving techniques and to practise the methods learnt in this module. They also allows the assessment of the computational skills acquired by the student. The PC tests allow the students to assess their progress with the material. They both allow feedback to the students and so act as formative as well as summative assessment.

Reading Lists