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Mathematical methods, models and modelling

Solve real problems by finding out how they are transformed into mathematical models and learning the methods of solution. This module covers classical mechanical models as well as some non-mechanical models such as population dynamics; and methods including vector algebra, differential equations, calculus (including several variables and vector calculus), matrices, methods for three-dimensional problems, and numerical methods. Teaching is supported and enhanced by use of a computer algebra package. This module is essential for higher level study of applied mathematics. To study this module you’ll need a sound knowledge of mathematics as developed in Essential mathematics 1 (MST124) and Essential mathematics 2 (MST125) or equivalent.

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying MST210 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

Modules count towards OU qualifications

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
MST210
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.
60
Study level

Across the UK, there are two parallel frameworks for higher education qualifications, the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ) and the Scottish Credit and Qualifications Framework (SCQF). These define a hierarchy of levels and describe the achievement expected at each level. The information provided shows how OU module levels correspond to these frameworks.

OU SCQF FHEQ
2 9 5
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
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What you will study

This module will be of particular interest to you if you use mathematics or mathematical reasoning in your work and feel that you need a firmer grounding in it, or if you think you might find it useful to extend your application of mathematics to a wider range of problems. The module is also very suitable for those planning to teach applied mathematics.

Around half of this module is about using mathematical models to represent suitable aspects of the real world; the other half is about mathematical methods that are useful in working with such models. The work on models is devoted mainly to the study of classical mechanics, although non-mechanical models – such as those used in population dynamics – are also studied. The process of mathematical modelling, based on simplifying assumptions about the real world, is outlined. You will work in groups to create a mathematical model and to produce a mini-report. The work on methods comprises topics chosen for their usefulness in dealing with the models; the main emphasis is on solving the problems arising in the real world, rather than on axiom systems or rigorous proofs. These methods include differential equations, linear algebra, advanced calculus and numerical methods. 

You’ll begin the mechanics part of the module with statics, where there are forces but no motion, and then you’ll be introduced to the fundamental laws governing the motions of bodies acted on by forces – Newton's laws of motion. These are applied to model:

  • the motion of a particle moving in a straight line under the influence of known forces
  • undamped oscillations
  • the motion of a particle in space
  • the motions of systems of particles
  • the damped and forced vibrations of a single particle
  • the motion (and vibrations) of several particles.

In the methods part of the module you’ll cover both analytic and numerical methods. You’ll explore the analytical (as opposed to numerical) solution of first-order and of linear, constant-coefficient, second-order ordinary differential equations, followed by systems of linear and non-linear differential equations and an introduction to methods for solving partial differential equations. The topics in algebra are vector algebra, the theory of matrices and determinants, and eigenvalues and eigenvectors. You’ll develop the elements of the calculus of functions of several variables, including vector calculus and multiple integrals, and make a start on the study of Fourier analysis. Finally, the study of numerical techniques covers the solution of systems of linear algebraic equations, methods for finding eigenvalues and eigenvectors of matrices, and methods for approximating the solution of differential equations.

You will learn

Successful study of this module should improve your skills in being able to think logically, express ideas and problems in mathematical language, communicate mathematical arguments clearly, interpret mathematical results in real-world terms and find solutions to problems.

Professional recognition

This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.

Teaching and assessment

Support from your tutor

You will have a tutor who will help you with the study material and 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 or day-schools in your locality that you are encouraged, but not obliged, to attend, and there is an online forum. Where your 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

Mathematical methods, models and modelling 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 2021.

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:

    8 Tutor-marked assignments (TMAs)
    Examination
    No residential school

    Course satisfaction survey

    See the satisfaction survey results for this course.


    Entry requirements

    To study this module, normally you should have completed Essential mathematics 2 (MST125) or the discontinued module MS221.

    There may be circumstances in which you can study this module without having first studied MST125, but you should speak to an adviser to discuss this before registering on this module.

    Knowledge of mechanics is not needed, but we do not recommend the module if you have little mathematical experience. You need a good basic working knowledge of: 

    • algebra – you must be able to solve linear and quadratic equations with one unknown, to multiply and add polynomials, to factorise quadratic polynomials and to work with complex numbers
    • geometry – you must know Pythagoras' theorem and how to use Cartesian coordinates, e.g. the equations of straight lines and circles 
    • trigonometry – you need to know the basic properties of the three trigonometric ratios sine, cosine and tangent, and the definitions of the corresponding inverse functions
    • calculus – you must be able to differentiate and integrate a variety of functions, though great facility in integration is not necessary
    • mechanics – you should have some basic knowledge of Newtonian mechanics.

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

    Register

    Start End England fee Register
    06 Oct 2018 Jun 2019 £2928.00

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

    Register
    This module is expected to start for the last time in October 2021.

    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 or book a call back at a time convenient to you.


    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 22/07/2018.

    What's included

    Module books, other printed materials, algebra software, and module website.

    You will need

    You require internet access at least once a week during the module to download module resources and assignments, and to keep up to date with module news.

    A calculator – you may wish to use this during the module, but you are not allowed to take a calculator into the examination.

    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

    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

    Written transcripts of any audio components and Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader (mathematical notation may be particularly difficult to read in this way). Other alternative formats of the study materials may be available in the future. 

    It is important to note that use of the module software, which includes on-screen graphs and mathematical notation, will be an integral part of your study. You will need to spend considerable amounts of time using a personal computer. If you use specialist hardware or software to assist you in using a computer you are advised to contact us about support which can be given to 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.