Mathematical methods and models
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| 7 Tutor-marked assignments (TMAs) | 2 Computer-marked assignments (CMAs) |
| Examination | No residential school |
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Summary
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 heat transfer and 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).
Course content
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 2001i.
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 2001i, 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-point one week residential school course Mathematical modelling (MSXR209) consolidates and extends this course, enabling you to develop your own mathematical models. If you are taking the B31 Mathematics degree then you will need to do MSXR209. 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 points of study in one academic year, then you can study MSXR209 later.
Entry
MST209 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. You need no knowledge of mechanics, but the course is not recommended if you have little mathematical experience. You need a good basic working knowledge of algebra, geometry, trigonometry and calculus. In 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. In geometry you must know Pythagoras's theorem and how to use Cartesian coordinates, e.g. the equations of straight lines and circles. In 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. In calculus you must be able to differentiate and integrate a variety of functions, though great facility in integration is not necessary. A diagnostic quiz that will enable you to determine whether you are adequately prepared for this course can be found on the website.
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 2001i 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.
Qualifications
MST209 is a compulsory course in our
- BA/BSc (Honours) Mathematics (B31)
- Diploma in Mathematics (D23)
- BSc (Honours) Mathematics and its Learning (B46)
MST209 is an optional course in our
- BA/BSc (Honours) Mathematics and Statistics (B36)
- BA/BSc (Honours) Computing and Mathematical Sciences (B14)
- BA/BSc (Honours) Economics and Mathematical Sciences (B15)
- BSc (Honours) Physical Science (B27)
- BSc (Honours) Secondary Education in Physics (B56)
- Diploma in Physical Science (E04)
- Diploma in Statistics (D44)
It can also count towards most of our other degrees at bachelors level, where it is equally appropriate to a BA or BSc. We advise you to refer to the relevant qualification descriptions for information on the circumstances in which this course can count towards these qualifications because from time to time the structure and requirements may change. You are also advised to check carefully whether or not the Award towards which you are studying requires you to also study Mathematical modelling (MSXR209), as you may wish to study it in the same year as MST209.
Excluded combinations
Sometimes you will not be able to count a course towards a qualification if you have already taken another course with similar content. To check any excluded combinations relating to this course, visit our excluded combination finder or check with our Student Registration & Enquiry Service before registering.
If you have a disability or additional requirement
Transcripts for the DVD-video are available on the course website and the multi-media material on the course DVD includes embedded transcripts. The printed course 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 course materials are available on audio in DAISY Digital Talking Book format. Large print versions of the printed course material can be provided on request. 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 booklet Meeting Your Needs which you can download or request from our Student Registration & Enquiry Service.
You can also find information about accessible course 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.
Course materials
What's included
Course books, other printed materials, DVD, Mathcad 2001i, course 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 2002 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 Boot Camp or similar.
Teaching and assessment
Support from your tutor
You will have a tutor who will help you with the course 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.
Assessment is an essential part of the teaching, so you are expected to complete it all. But if you unavoidably miss or do badly in an assignment, some courses allow you a 'substitution score'. In MST209 this rule can apply to one TMA and one CMA. You will be given more detailed information when you begin the course.
Professional recognition
This course may help you to gain recognition from a professional body. You can download our Recognition leaflets 3.6 Institute of Mathematics and its Applications, 3.7 Computing, 3.8 Scientific Institutions, or ask our Student Registration & Enquiry Service for a copy.
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 January 2011. We expect it to be available at the same time once a year.
How to register
To register a place on this course return to the top of the page and use the Click to register button. For more information and advice about registration see OU Study Explained.
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An undergraduate course in Engineering and Technology, Mathematics and Statistics and Science.
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