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.

Course facts
About this course:
Course code MST210
Credits 60
OU Level 2
SCQF level 9
FHEQ level 5
Course work includes:
8 Tutor-marked assignments (TMAs)
No residential school

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.


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.

If you have a disability or additional requirement

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.

Study materials

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

You will need a device with internet access to study this module as a web browser is used to access learning materials and activities. Any other computer-based activities you will need to carry out, such as word processing, using spreadsheets, taking part in online forums, and submitting files to the university for assessment, are specified in the module materials. If any additional software is needed for these tasks it will either be provided or is freely available. You may need administrative privileges to install software required for this module. Windows 10 S is not suitable as it restricts software installation to software available in the Windows Application Store.

Suitable devices are:

  • A Windows desktop or laptop running Windows 7 or later operating system
  • A Macintosh desktop or laptop running OS X 10.8 or later operating system.

Some software will not run on Linux, iOS or Android devices.

A netbook, tablet, smartphone or Linux computer that supports one of the browsers listed below may be suitable. However, these devices may not be suitable for some activities. If you intend to use one of these devices please ensure you have access to a suitable desktop or laptop device that uses the Windows or OS X operating system in case you are unable to carry out all activities on your mobile device.

Recent versions of the following browsers are suitable for carrying out web-based activities:

  • Safari
  • Chrome
  • Firefox
  • Edge

Or Internet Explorer 9 and above.

Using a browser upgraded to the latest version will maximise security when accessing the internet.

Using company or library computers may prevent you accessing some internet materials or installing additional software.

To be able to talk and listen in our online discussions you will need both a microphone and speakers/headphones.

Devices with small screens may make it difficult to view the material provided and carry out the activities. However, a device that has a resolution of at least 1024 pixels horizontally and also at least 768 pixels vertically should be adequate.

See our Skills for OU study website for further information about computing skills for study and educational deals for buying Microsoft Office software.

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.


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

The details given here are for the module that starts in October 2017. It starts once a year – in October.

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

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.