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Deterministic and stochastic dynamics

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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.

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.

Read the full content list here.

Entry requirements

There is no formal pre-requisite study, but you must have the required mathematical skills.

Preparatory work

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:

• differential equations
• mechanics.

Mathematical methods, models and modelling (MST210) or Mathematical methods (MST224) is ideal preparation.

What's included

• a week-by-week study planner
• course-specific module materials
• audio and video content
• Maxima algebra software and associated guidance
• assessment details, instructions and guidance
• online tutorial access

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.

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 an up-to-date version of Windows, macOS or Linux.

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

To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).

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

You'll have a tutor who will help you with the study material and mark and comment on your written work, and who you can ask for advice and guidance. Your tutor can also provide additional assistance with your study skills, especially if you're new to OU study.

Tutorials are designed to aid student success by providing help and guidance with your studies, including hints and tips to improve your understanding. You are encouraged to attend as many as you can – whether face-to-face or online they are an informal way to ask questions and to feel part of a student community.

We aim to provide face-to-face tutorials in a range of locations students can travel to, though we cannot guarantee availability close to where you live. An online alternative, covering similar content, is usually provided, typically with a recording of at least one such online tutorial being made available.

Student numbers on the module, and where tutors are based, will affect which tutor may lead a particular tutorial, the locations of face-to-face tutorials, and what online alternatives are offered.

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.

If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying MS327 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

Future availability

Deterministic and stochastic dynamics (MS327) starts once a year – in October.