Deterministic and stochastic dynamics is designed to be studied as your first applied mathematics module at OU level 3. It introduces core topics in applied mathematics at this level and is structured around three books: Fundamental concepts of dynamics; Deterministic dynamics; and Stochastic processes and diffusion. The module will use the Maxima computer algebra system to illustrate how computers are used to explore properties of dynamical systems. To study this module, you should have a good prior knowledge of the subject area, including differential equations, and some knowledge of mechanics, as provided by the appropriate OU level 2 study.
| Course facts | |
|---|---|
| About this course: | |
| Course code | MS327 |
| Credits | 30 |
| OU Level | 3 |
| SCQF level | 10 |
| FHEQ level | 6 |
| Course work includes: | |
| 4 Tutor-marked assignments (TMAs) | |
| Examination | |
| No residential school | |
This module is presented as three books.
Book 1: Fundamental concepts of dynamics
The first book considers ordinary differential equations, Newton's second law, conservation of energy, and the concepts of fixed point, limit cycles and constants of motion. It will also introduce a framework for discussing random processes, such as random walks.
Book 2: Deterministic dynamics
The second book will develop some more advanced concepts. In the case of conservative systems, it introduces the calculus of variations and develops Lagrangian dynamics from Hamilton's principle. In the case of dissipative systems, it will consider the use of maps to model dynamical processes. 'Chaos' will be defined and explored using the strange attractor. The book will introduce the notions of Lyapunov exponents, fractal dimensions of attractors, and their connection via the 'Lyapunov dimension' formula.
Book 3: Stochastic processes and diffusion
Finally, the third book will investigate the random walk as the archetypical random dynamical process, and explain its connection to the diffusion equation. Fourier methods (both series and transforms) will be treated by illustrating their role in treatment of the diffusion equation and probability theory. The module will conclude with a look at some further applications of random dynamical systems, including the models used for option pricing in mathematical finance.
The module will use the Maxima computer algebra system to illustrate how computers are used to explore properties of dynamical systems. You will be required to use Maxima in some of the assignments, but it will be possible to complete the module without very extensive use of this package. However, there will be plenty of optional exercises which illustrate the power of computers for exploring the properties of dynamical systems.
You can find the full content list on the Open mathematics and statistics website.
Understanding how to analyse dynamical processes is a central competence for using mathematics in science, engineering, and economics. Mastering the material in this module will give you powerful tools used by practising applied mathematicians.
There is no formal pre-requisite study, but you must have the required mathematical skills.
You can check you're ready for MS327 and see the topics it covers here.
Talk to an advisor if you're not sure you're ready.
You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.
The key topics to revise include:
Mathematical methods, models and modelling (MST210) or Mathematical methods (MST224) is ideal preparation.
You'll have access to a module website, which includes:
You'll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You'll also receive a printed module handbook.
A scientific calculator.
You'll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Monterey or higher.
Any additional software will be provided or is generally freely available.
To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).
Our module websites comply with web standards, and any modern browser is suitable for most activities.
Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It's not available on Kindle.
It's also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you'll also require a desktop or laptop, as described above.
Throughout your module studies, you'll get help and support from your assigned module tutor. They'll help you by:
Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won't be compulsory for you to complete the module, you're strongly encouraged to take part.
The assessment details for this module can be found in the facts box.
The OU strives to make all aspects of study accessible to everyone. The Accessibility Statement below outlines what studying this module involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.
Printed materials are provided for the core module text. All of this module's study materials are also online; this includes PDFs of any printed materials, plus some items which are only provided online. Online-only materials include video clips (with transcripts) and self-assessed quizzes. Online materials also include links to external resources, online forums and online tutorial rooms. This module uses mathematical/statistical software.
This module has online tutorials. Although not compulsory, tutorials will help you consolidate your learning.
Mathematical and scientific symbols and expressions are used throughout the module and you will be required to use such notation within assessment.
The study materials contain a considerable number of diagrams and graphs. Interpreting and producing examples of these is an important part of the study of this module and is assessed. Figure descriptions are provided for most figures.
In this module you will be working with specialist reading material which includes mathematical notation. This is delivered both online and in printed form, and also via bespoke and third party software.
This module has Tutor-Marked Assignments (TMAs), which can be submitted online via the OU electronic TMA system or by post, Interactive Computer Marked Assignments (iCMAs) completed online, and an Exam that you will take remotely.
You will receive feedback from your tutor on your submitted Tutor-Marked Assignments (TMAs). This will help you to reflect on your TMA performance. You should refer to it to help you prepare for your next assignment.
All University modules are structured according to a set timetable and you will need time-management skills to keep your studies on track. You will be supported in developing these skills.
MS327 uses the computer algebra system, Maxima. It is possible to use a command line interface for Maxima. The interactive applets have some accessibility controls, but you may need the support of a non-medical helper. Some accessibility advice is provided for the software activities in the Module Guide and the Computer Algebra Guide, but if you have any concerns, please contact us.
Deterministic and stochastic dynamics (MS327) starts once a year – in October.
This page describes the module that will start in October 2024.
We expect it to start for the last time in October 2027.
This course is expected to start for the last time in October 2027.