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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.

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OU qualifications are modular in structure; the credits from this undergraduate module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

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Module

Module code
MS327
Credits

Credits

  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
30
Study level
3
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
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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.

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.

Regulations

As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Essential Documents website.

    Course work includes:

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

    Course satisfaction survey

    See the satisfaction survey results for this course.


    Entry requirements

    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.

    Register

    Start End England fee Register
    06 Oct 2018 Jun 2019 £1464.00

    Registration closes 13/09/18 (places subject to availability)

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

    Additional Costs

    Study costs

    There may be extra costs on top of the tuition fee, such as a laptop, travel to tutorials, set books and internet access.

    If you're on a low income you might be eligible for help with some of these costs after your module has started.

    Ways to pay for this module

    Open University Student Budget Account

    The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

    You pay the OU through OUSBA in one of the following ways:

    • Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.
    • Pay by instalments – OUSBA calculates your monthly fee and number of instalments based on the cost of the module you are studying. APR 5.1% representative.

    Joint loan applications

    If you feel you would be unable to obtain an OUSBA loan on your own due to credit history or affordability issues, OUSBA offers the option to apply for a joint loan application with a third party. For example, your husband, wife, partner, parent, sibling or friend. In such cases, OUSBA will be required to carry out additional affordability checks separately and/or collectively for both joint applicants who will be jointly and severally liable for loan repayments.

    As additional affordability checks are required when processing joint loan applications, unfortunately, an instant decision cannot be given. On average the processing time for a joint loan application is five working days from receipt of the required documentation.

    Read more about Open University Student Budget Accounts (OUSBA).  

    Employer sponsorship

    Studying with The Open University can boost your employability. OU courses are recognised and respected by employers for their excellence and the commitment they take to complete. They also value the skills that students learn and can apply in the workplace.

    More than one in ten OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the module you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees. 

    • Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.
    • You won’t need to get your employer to complete the form until after you’ve chosen your module.  

    Credit/debit card

    You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module. 

    We accept American Express, Maestro (UK only), Mastercard, Visa/Delta and Visa Electron. 

    Mixed payments

    We know that sometimes you may want to combine payment options. For example, you may wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Account (OUSBA).

    For more information about combining payment options, speak to an adviser.


    Please note: your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fees and funding information provided here is valid for modules starting before 31 July 2019. Fees normally increase annually in line with inflation and the University's strategic approach to fees. 

    This information was provided on 21/06/2018.

    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
    • Mac OS 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. 

    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.

    To find out more about what kind of support and adjustments might be available, contact us or visit our Overcoming barriers to study if you have a disability or health condition website.