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)
Examination
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.

Entry

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.

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

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.

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.

If you have a disability

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

Mode of study

Printed materials are provided for the core module text. All of this module's study materials are also online; this includes PDFs of any printed materials, plus some items which are only provided online. Online-only materials include audio/video clips (with transcripts/subtitles) and diagrams. Online materials also include links to external resources, online forums and online tutorial rooms. This module uses mathematical/statistical software.

Tuition strategy

This module provides a range of face-to-face and online learning events. Each face-to-face learning event offers an online (or other) alternative. Although not compulsory, attendance at tutorials will help you consolidate your learning.

Working with others

You will be required to work with other students as part of a mathematical modelling activity. A few marks are allocated for this group work, but the majority of the marks are allocated individually to the modelling report you produce at the end of this activity.

Mathematical and scientific expressions and notations

Mathematical and scientific symbols and expressions are used throughout the module and you will be required to use such notation within assessment.

Diagrams and other visual content

The study materials contain a considerable number of diagrams, especially in the texts concerned with Newtonian mechanics. Interpreting and producing examples of these is an important part of the study of this module and is assessed. Figure descriptions are provided for most figures.

Finding information

You may be required to search for, and make use of, third party material online as part of the mathematical modelling activity and this is assessed as part of this activity. This searching is done as part of the group activity and other group members should be able to help with this.

Specialist reading material

In this module you will be working with specialist reading material containing mathematical notation and mathematical diagrams. These are delivered mainly in printed form, but with some material online.

Assessment

This module has Tutor-Marked Assignments (TMAs), which can be submitted online via the OU electronic TMA system, or by post. It also has an exam that must be taken at an exam centre.

Feedback

You will receive feedback from your tutor on your submitted Tutor-Marked Assignments (TMAs). This will help you to reflect on your TMA performance. You should refer to it to help you prepare for your next assignment.

Schedule

All University modules are structured according to a set timetable and you will need time-management skills to keep your studies on track. You will be supported in developing these skills.

Specialist software

MST210 uses the computer algebra system, Maxima. It is possible to use a command line interface for Maxima. The interactive applets have some accessibility controls, but you may need the support of a non-medical helper. Some accessibility advice is provided for the software activities in the Module Guide and the Computer Algebra Guide, but if you have any concerns, please contact us.

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.

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.