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Mathematical methods and models

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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. To study this module you should have a sound knowledge of relevant mathematics as provided by the appropriate Level 1 study.

Modules at Level 2 assume that you are suitably prepared for study at this level. If you want to take a single module to satisfy your career development needs or pursue particular interests, you don’t need to start at Level 1 but you do need to have adequately prepared yourself for OU study in some other way. Check with our Student Registration & Enquiry Service to make sure that you are sufficiently prepared.

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No current presentation - see Future availability

This course is expected to start for the last time in October 2013.

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 should also be suitable if you are teaching A-level applied mathematics, or if you intend to do so; the material on mechanics, in particular, gives a very careful treatment of the basic concepts of this subject. The teaching is supported and enhanced by the computer algebra package Mathcad.

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 heat transfer and population dynamics – are also studied. 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. Many are implemented in Mathcad, so you can use the computer to solve more difficult problems and to investigate case studies.

The mechanics part of the module begins with statics, where there are forces but no motion, and then introduces the fundamental laws governing the motions of bodies acted on by forces – Newton's laws of motion. These are first applied to model the motion of a particle moving in a straight line under the influence of known forces. Undamped oscillations are discussed next. Newton's laws are then extended to the motion of a particle in space. The motions of systems of particles are modelled. Next we look at the damped and forced vibrations of a single particle. Then we look at the motion (and vibrations) of several particles. Finally, we investigate the motion of rigid bodies.

The methods part of the module covers both analytic and numerical methods. The analytical (as opposed to numerical) solution of first-order and of linear, constant-coefficient, second-order ordinary differential equations is discussed, 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. We 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.


This is a Level 2 module and you need a good knowledge of the subject area, obtained either from Level 1 study with the OU or from equivalent work at another university. 

It is designed to follow both Using mathematics (MST121) and Exploring mathematics (MS221). You are more likely to successfully complete this Level 2 module if you have acquired your prerequisite knowledge through passing these modules. You are advised to obtain a good pass in both modules first, or to make sure that you have reached an equivalent standard. If you have only passed MST121 we can provide some study material to help you bridge the gap to MST209. The bridging material is available on the MST209 module website.

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's 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. 

Our diagnostic quiz Am I ready to start on MST209? will help you to determine whether you are adequately prepared for this module.

Your regional or national centre will be able to tell you where you can see reference copies of the study materials, or you can buy selected texts from Open University Worldwide Ltd. If you have any doubt about the suitability of the module, please contact our Student Registration & Enquiry Service.

Preparatory work

The module starts with an introductory unit that enables you to revise the necessary topics (see Entry), but it is not suitable for learning them for the first time. You will need to familiarise yourself with the module software and Mathcad by studying a computer booklet and associated files that come in the first mailing. The time that takes will vary according to your experience with Mathcad.


As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are available on our Essential documents website.

If you have a disability

Transcripts for the DVD-video are available on the website and the multi-media material on the DVD includes embedded transcripts. The printed study material is available in comb-bound format.  Adobe Portable Document Format (PDF) versions of printed material are also available.  However, some Adobe PDF components may not be available or fully accessible using a screen reader and formula, diagrams and certain mathematical elements may be particularly difficult to read in this way. The study materials are available on audio in DAISY Digital Talking Book format. Other formats may be available in the future. Our Services for disabled students website has the latest information about availability.

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 have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Visit our Services for disabled students website for more information, including:

  • help to determine your study requirements and how to request the support that you need  
  • Disabled Students' Allowances (DSAs)
  • using a computer for OU study
  • equipment and other support services that we offer
  • examination arrangements
  • how to contact us for advice and support both before you register and while you are studying.

Study materials

What's included

Module books, other printed materials, DVD, Mathcad, website.

You will need

You require internet access at least once a week during the module to download module resources and assignments, keep up to date with module news and submit the computer-marked assignments (CMAs).

DVD player (optional - you can watch the DVD video on your computer if you have a DVD drive and appropriate software).

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

You will need a computer with internet access to study this course. It includes online activities – you can access using a web browser – and some course software provided on disk.

  • If you have purchased a new desktop or laptop computer running Windows since 2007 you should have no problems completing the computer-based activities.
  • A netbook, tablet or other mobile computing device is not suitable for this course – check our Technical requirements section.
  • If you have an Apple Mac or Linux computer – please note that you can only use it for this course by running Windows on it using Boot Camp or a similar dual-boot system.

You can also visit the Technical requirements section for further computing information including the details of the support we provide.

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 our Student Registration & Enquiry Service if you want to know more about study with The Open University before you register.


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

Please note that TMAs for all undergraduate mathematics and statistics modules must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system. You will need to submit CMAs electronically, using the eCMA system.

Future availability

The details given here are for the module that starts in October 2013 when it will be available for the last time. A new module, Mathematical methods, models and modelling (MST210), is available from October 2014.

Students also studied

Students who studied this course also studied at some time:

How to register

We regret that we are currently unable to accept registrations for this course. Where the course is to be presented again in the future, relevant registration information will be displayed on this page as soon as it becomes available.

Student Reviews

“Very tough and very rewarding. Had to put in lots of hours each week to keep up with the pace ...”
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“I took this as preparation for third level physics modules and really enjoyed it. Whilst there is a large spread ...”
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Distance learning

The Open University is the world’s leading provider of flexible, high quality distance learning. Unlike other universities we are not campus based. You will study in a flexible way that works for you whether you’re at home, at work or on the move. As an OU student you’ll be supported throughout your studies – your tutor or study adviser will guide and advise you, offer detailed feedback on your assignments, and help with any study issues. Tuition might be in face-to-face groups, via online tutorials, or by phone.

For more information read Distance learning explained.

Are you already an OU student ? Go to StudentHome for information on choosing your next module.
Course facts
About this course:
Course code MST209
Credits 60
OU Level 2
SCQF level 9
FHEQ level 5
Course work includes:
7 Tutor-marked assignments (TMAs)
2 Computer-marked assignments (CMAs)
No residential school

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