MA4DSA: Dynamical Systems and Applications

Module code: MA4DSA

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 4 (Undergraduate Masters)

When you'll be taught: Semester 2

Module convenor: Dr Peter Chamberlain, email: p.g.chamberlain@reading.ac.uk

Module co-convenor: Professor Marcus Tindall, email: m.tindall@reading.ac.uk

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST TAKE MA2DE (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded: IN TAKING THIS MODULE YOU CANNOT TAKE MA3DSA OR TAKE MA3DS OR TAKE MA3MB (Compulsory)

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

This module will provide an introduction to the analysis of dynamical systems and their application to real-world problems. The module will first take a look at two variable linear systems of ordinary differential equations (ODEs) before moving onto nonlinear ones, investigating the overall system dynamics via steady-state stability and phase plane analysis. Applications of the relevant theory will then be applied in the second half of the module to biological problems covering population growth, cell systems, the spread of infectious diseases before closing with a look at the dynamical behaviour of nonlinear partial differential equation (PDE) models describing biological waves and patterns. 

Module learning outcomes

By the end of the module students are expected to be able to:

1. Analyse the structure of planar autonomous and non autonomous linear and nonlinear dynamical systems;
2. Apply steady-state stability and phase plane analysis and manifold theory;
3. Apply the analysis of nonlinear dynamical systems, using bifurcation theory where appropriate, to problems in biology; and
4. Utilising the results of mathematical analysis, provide insight into biological systems.

Module content

• Steady-state stability analysis
• The phase plane - Plotting phase fields and trajectories
• Analysing systems of 2 first order linear ODEs
• Analysing systems of 2 first order nonlinear ODEs
• Manifold theory
• Single species population models
• Two species population models and bifurcation theory
• Mathematical models of cell regulation
• Understanding the spread of infectious diseases
• Analysing nonlinear PDE models of biological phenomena (e.g. genetic variation)
• Pattern formation and Turing systems
• Problems in drug delivery

Structure

Teaching and learning methods

The material is delivered via lectures supported by tutorials with formative exercises. Feedback on formative exercises will be provided to support learning.

A weekly one hour online office hour complemented with some short screencasts on specific chosen topics, where relevant.

Study hours

At least 50 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 50% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: https://www.reading.ac.uk/cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Non-assessed problem sheets 

Reassessment

Additional costs