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 course 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. You are assumed to have a sound knowledge of mathematics as developed in Using mathematics (MST121) and parts of Exploring mathematics (MS221).
Fees 2012
See fees and funding options for study from September 2012.
Course facts
An undergraduate course in Engineering and Technology , Mathematics and Statistics and Science.
| 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) |
| Examination |
| No residential school |
Register for the course
This course is available for study in the countries shown. Fees and financial support may vary by country.
What you will study
This course 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 course 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 course 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 course 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 course 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.
Associated residential school course
The 10-credit one week residential school course Mathematical modelling (MSXR209) consolidates and extends this course, enabling you to develop your own mathematical models. MSXR209 is compulsory if you are studying towards the BA/BSc (Hons) Mathematics degree. In this case because the courses are designed to complement each other, you may like to consider doing them in the same year, although you should carefully consider the workload implications. If you feel that you cannot undertake 70 credits of study in one academic year, then you can study MSXR209 later.
You will learn
Successful study of this course 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
This is a Level 2 course 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.
Knowledge of mechanics is not needed, but we do not recommend the course 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 course.
The course is designed to follow Using mathematics (MST121) and Exploring mathematics (MS221). Students are more likely to complete this course successfully if they have acquired their prerequisite knowledge through passing those courses. You are advised to obtain a good pass in both of those courses first, or to make sure that you have reached an equivalent standard. If you have passed MST121, but not MS221 then there is some study material available to help you bridge the gap. The bridging material is available on the website.
The online quiz will indicate whether or not you need to study this. Your regional or national centre will be able to tell you where you can see reference copies of the courses, or you can buy selected texts from Open University Worldwide Ltd. If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
Preparatory work
The course 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 course 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.
If you have a disability or additional requirement
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 course 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 are a new student, or new to courses using a computer or the internet, you will need to inform us of your particular needs as soon as possible, as some of our support services may take several weeks to arrange. Details of how to do this and our range of support services are described in our publication Meeting Your Needs.
You can also find information about accessible study materials, financial support and the Disabled Students' Allowance, equipment and other services, on our Services for disabled students website. It also includes our contact details for advice and support both before you register and while you are studying.
Study materials
What's included
Course books, other printed materials, DVD, Mathcad, website.
You will need
You require internet access at least once a week during the course to download course resources and assignments, keep up to date with course 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 course, but you are not allowed to take a calculator into the examination.
Computing requirements
This course includes online computer activities – you can access these using a web browser that can play Flash and Shockwave. Some of your course software will be provided on disk.
You will need internet access and a computer. If you have purchased a new Windows computer since 2005 it should meet your course computing requirements. Check our Technical Requirements section if your computer is older than this or is otherwise unusual. Please note that you cannot use an Apple Mac or Linux computer unless it is running Windows using Boot Camp or similar dual-boot system.
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 course. Contact our Student Registration & Enquiry Service if you want to know more about study with The Open University before you register.
Assessment
The assessment details for this course can be found in the facts box above.
Please note that TMAs for all undergraduate mathematics and statistics courses 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.
Professional recognition
This course may help you to gain recognition from a professional body. You can view or download our Recognition leaflets 3.6 Institute of Mathematics and its Applications, 3.7 Computing, 3.8 Scientific Institutions for further information.
Students also studied
Students who studied this course also studied at some time:
Future availability
The details given here are for the course that starts in October 2012. We expect it to be available once a year.
Fees 2012
See fees and funding options for study from September 2012.
Course facts
An undergraduate course in Engineering and Technology , Mathematics and Statistics and Science.
| 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) |
| Examination |
| No residential school |
Study explained
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- - find out if you qualify for support with your fees with our eligibility checker.
- Study explained
- - all you need to know about distance learning with the OU.
Student Reviews
A broad course which introduces many techniques useful for future study. The TMAs are well-spaced and a fair reflection of ...
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A good course for an introduction to mechanics using vector calculus, matrices and partial differential equations. The course title pretty ...
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