Deterministic and stochastic dynamics

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)
4 Interactive computer-marked assignments (iCMAs)
Examination
No residential school

What you will study

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.

Vocational relevance

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.

Entry

This is an OU level 3 module. OU level 3 modules build on study skills and subject knowledge acquired from studies at OU levels 1 and 2. They are intended only for students who have recent experience of higher education in a related subject, preferably with the OU.

Deterministic and stochastic dynamics is designed to be studied as your first applied mathematics module at OU level 3, following on from Mathematical methods, models and modelling (MST210) (or its predecessor MST209) or Mathematical methods (MST224).

You will need a good knowledge of the subject area including differential equations and some mechanics, obtained either from OU level 2 study as described above or from equivalent work at another university.

You can try our diagnostic quiz to help you determine whether you are adequately prepared for this module.

If you have any doubt about the suitability of the module, please speak to an adviser.

Preparatory work

There is no specific preparatory work required for this module but it may be helpful for you to revise differential equations and mechanics before the module begins.

If you have a disability or additional requirement

The mathematical equations in the module text are not currently accessible to a screen reader, but electronic versions of the books (PDFs, ePubs) will be available in the future. However, mathematics read in this way may be difficult to understand.

Figure descriptions will be available, as well as written transcripts of any audio component. Other alternative formats of the study materials may be available in the future.

Study materials

What's included

Printed module books, a printed handbook, other support materials on a module website and assessment materials.

You will need

A scientific calculator.

Computing requirements

A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

A desktop or laptop computer with either:

  • Windows 7 or higher
  • macOS 10.7 or higher
  • a modern Linux version

The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

To participate in our online-discussion area you will need both a microphone and speakers/headphones.

Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.

Teaching and assessment

Support from your tutor

You will have a tutor who will mark and comment on your written work, and whom you can ask for advice and guidance. We may also be able to offer group tutorials (either face-to-face or online) or day schools that you are encouraged, but not obliged, to attend. Where your face-to-face tutorials are held will depend on the distribution of students taking the module.

Contact us if you want to know more about study with The Open University before you register.

Assessment

The assessment details for this module can be found in the facts box above.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

Future availability

Deterministic and stochastic dynamics starts once a year – in October. This page describes the module that will start in October 2018. We expect it to start for the last time in October 2023.

This course is expected to start for the last time in October 2023.