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 | |
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:
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 can find the full content list on the Open mathematics and statistics website.
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.
You must have passed the following module:
Or be able to provide evidence you have the required mathematical skills.
You can check you're ready for MST210 and see the topics it covers here.
Talk to an advisor if you're not sure you're ready.
You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.
The key topics to revise include:
Essential mathematics 2 (MST125) is ideal preparation.
You'll have access to a module website, which includes:
You'll also be provided with six printed books and a printed module handbook.
A calculator – you may wish to use this during the module, but you are not allowed to take a calculator into the examination.
You'll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Monterey or higher.
Any additional software will be provided or is generally freely available.
To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).
Our module websites comply with web standards, and any modern browser is suitable for most activities.
Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It's not available on Kindle.
It's also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you'll also require a desktop or laptop, as described above.
Throughout your module studies, you'll get help and support from your assigned module tutor. They'll help you by:
Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won't be compulsory for you to complete the module, you're strongly encouraged to take part.
The assessment details for this module can be found in the facts box.
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.
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.
This module has online tutorials. Although not compulsory, tutorials will help you consolidate your learning.
You will have the opportunity 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 symbols and expressions are used throughout the module and you will be required to use such notation within assessment.
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.
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.
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.
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 you will take remotely.
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.
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.
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.
Mathematical methods, models and modelling (MST210) starts once a year – in October.
This page describes the module that will start in October 2024.
We expect it to start for the last time in October 2025.
This course is expected to start for the last time in October 2027.
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.