UNIVERSITY OF KENT
MODULE SPECIFICATION
SECTION 1: MODULE SPECIFICATIONS
1. Title of the module: Mathematical Modelling (MA590)
2. School or partner institution which will be responsible for management of the module
School of Mathematics, Statistics and Actuarial Science
3. Start date of the module: 2003 (revised version start date September 2014)
4. The number of students expected to take the module: 90
5. Modules to be withdrawn on the introduction of this proposed module and consultation with other relevant Schools and Faculties regarding the withdrawal
None; not applicable.
6. The level of the module (e.g. Certificate [C], Intermediate [I], Honours [H] or Postgraduate [M]): I
7. The number of credits and the ECTS value which the module represents : 15 (ECTS 7.5)
8. Which term(s) the module is to be taught in (or other teaching pattern): Autumn or Spring term
9. Prerequisite and co-requisite modules:
Prerequisite modules: MA321 Calculus and Mathematical Modelling, MA322 Proofs and Numbers, MA323 Matrices and Probability or MA326 Matrices and Computing
There are no co-requisite modules.
10. The programmes of study to which the module contributes
BSc (Hons) Mathematics, BSc (Hons) Mathematics & Statistics, BA (Hons) Mathematics and Accounting & Finance (including programmes with a year in industry), BSc (Hons) Mathematics with a Foundation Year, MMath Mathematics, MMathStat Mathematics and Statistics
11. The intended subject specific learning outcomes
On successful completion of this module students will:
a) have a reasonable knowledge of the various concepts and quantities required in population models and Newtonian mechanics;
b) be aware of how these quantities are linked by equations, using vectors and matrices where appropriate;
c) have a reasonable ability to derive and study these equations and interpret the results in terms of the original concepts;
d) have a reasonable ability to use MAPLE to illustrate the behaviour of population models;
e) appreciate the applications of Linear Algebra in mathematical modelling.
12. The intended generic learning outcomes
Students who successfully complete this module will have further developed:
a) an analytical approach to solving problems;
b) their ability to communicate solutions, simple proofs and calculations;
c) their numeracy and computational skills;
d) their ability to plan and carry out effective ways of studying.
13. A synopsis of the curriculum
1. Short introduction of Mathematical Modelling: modelling with data; deriving differential equations from data; dimensional analysis.
2. Revision of vector algebra and products of vectors (data types): dot product; vector product. Triple products of vectors: scalar triple product; vector triple product. Vector geometry: vector equations. Coordinate systems: cartesian, plane polar, cylindrical polar and spherical polar coordinates. Vector differentiation.
3. Discrete models and difference equations: steady states and their stability; linear difference equation and its applications.
4. Continuous models and ordinary differential equations: steady states and their stability; the slope fields and phase lines; continuous population models for a single species; application in mechanics: Newton’s laws for a single particle in 3-d; conserved quantities; angular velocity, angular momentum, moment of a force; harmonic motion.
5. Applications of Linear Algebra (in lower dimensions): systems of linear ordinary differential equations; linear phase plane analysis and stability; electrical networks.
14. Indicative Reading List
There is no single textbook that covers all aspects of the module. The following books cover various parts of the module.
· J Berry and K Houston, Mathematical Modelling, Edward Arnold
· D Edwards and M Hamson, Guide to Mathematical Modelling, Palgrave
· M Lunn, A First Course in Mechanics, Oxford University Press
· R K Nagle and E B Saff, Fundamentals of Differential Equations, Addison Wesley
· P J Oliver and C Shakiban, Applied Linear Algebra, Pearson
15. Learning and Teaching Methods, including the nature and number of contact hours and the total study hours which will be expected of students, and how these relate to achievement of the intended module learning outcomes.
Number of contact hours: 48 (36 lectures, 12 supervised classes)
Number of independent learning hours: 102.
Total study hours: 150.
During the classes the students tackle (unassessed) worksheets, but they will be asked to hand in solutions to some of these problems for their assessments. Some worksheet questions may require the use of MAPLE to develop an ability to solve unseen problems using computers, and to visualise and interpret their solutions effectively. Classes will also be used to discuss any difficulties that have arisen in lectures and to give feedback on assessments.
Subject specific learning outcomes 11(a)-(e) and generic learning outcomes 12(a)-(d) will be addressed by lectures and supervised classes.
16. Assessment methods and how these relate to testing achievement of the intended module learning outcomes
The module will be assessed by examination (80%) and coursework (20%).
Examination: A 2-hour written examination in the Summer Term that will consist of questions and numerical problems requiring short and long answers. The examination will test learning outcomes 11(a)-(c),(e) and 12(a)-(d).
Coursework: the students will be asked to hand in some worksheet problems for assessment. The coursework will test learning outcomes 11(a)-(e) and 12(a)-(d).
17. Implications for learning resources, including staff, library, IT and space
This is an existing module; no additional resources are required. The scheduling of the module will affect when the resources are required.
18. The School recognises and has embedded the expectations of current disability equality legislation, and supports students with a declared disability or special educational need in its teaching. Within this module we will make reasonable adjustments wherever necessary, including additional or substitute materials, teaching modes or assessment methods for students who have declared and discussed their learning support needs. Arrangements for students with declared disabilities will be made on an individual basis, in consultation with the University’s disability/dyslexiasupport service, and specialist support will be provided where needed.
19. Campus where module will be delivered: Canterbury
SECTION 2: MODULE IS PART OF A PROGRAMME OF STUDY IN A UNIVERSITY SCHOOL
Statement by the School Director of Learning and Teaching/School Director of Graduate Studies (as appropriate): "I confirm I have been consulted on the above module proposal and have given advice on the correct procedures and required content of module proposals"
......Director of Learning and Teaching/Director of Graduate Studies (delete as applicable)
…………………………………………………
Print Name / ......
Date
Statement by the Head of School: "I confirm that the School has approved the introduction of the module and, where the module is proposed by School staff, will be responsible for its resourcing"
......Head of School
…………………………………………………….
Print Name / ......
Date
Module Specification Template
Last updated February 2013
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