UNIVERSITY OF KENT
MODULE SPECIFICATION TEMPLATE
SECTION 1: MODULE SPECIFICATIONS
1. Title of the module: Orthogonal Polynomials and Special Functions (MA568)
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: September 2014
4. The number of students expected to take the module: 30
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 Modules to be withdrawn on the introduction of this proposed module and consultation with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: Honours [H]
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)
The module will run either in the Autumn Term or in the Spring Term.
9. Prerequisite and co-requisite modules
Pre-requisite modules: Stage 1 - MA321 (Calculus and Mathematical Modelling), MA322 (Proofs and
Numbers), MA323 (Matrices and Probability); Stage 2 - MA552 (Analysis), MA588 (Mathematical
Techniques and Differential Equations).
There are no co-requisite modules.
10. The programmes of study to which the module contributes
BSc (Hons) Mathematics, BSc (Hons) Mathematics and 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, MSc
Mathematics and its Applications.
11. The intended subject specific learning outcomes
On successful completion of this module, students will be able to:
a) understand the basic concepts of orthogonal polynomials and special functions;
b) have sound knowledge of inner products in L2-spaces as well as the skills to apply this knowledge
to problems in differential and difference equations;
c) understand how to apply the theory of analytical functions, differential and difference equations
and asymptotic methods.
12. The intended generic learning outcomes
On successful completion of the module, the students will have:
a) an enhanced ability to reason and deduce confidently from given definitions and constructions;
b) enhanced knowledge of special functions and their geometric, analytical and asymptotic
properties;
c) matured in their problem formulating and solving skills;
d) consolidated their grasp of a wide variety of mathematical skills and methods.
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UNIVERSITY OF KENT
13. A synopsis of the curriculum
This module builds on part of the material from MA588. It will start with an introduction to the
basics of special functions and orthogonal polynomials, including Gamma and Bessel functions
and their importance in physical problems.
Topics covered include:
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The hypergeometric functions, the parabolic cylinder functions, the confluent
hypergeometric functions (Kummer and Whittaker) explored from their series
expansions, analytical and geometrical properties, functional and differential equations
Orthogonal polynomials: from their definition to their properties
Classical polynomials and their applications as well as other hypergeometric-type
polynomials.
14. Indicative Reading List
The module does not follow a specific text. However, the following texts cover the material.
R. Askey, Orthogonal Polynomials and Special Functions, Society for Industrial and Applied
Mathematics, Philadelphia, PA, 1975
R. Beals and R. Wong, Special Functions – A Graduate Text, Cambridge University Press,
Cambridge, 2010
T.S. Chihara, An Introduction to Orthogonal Polynomials, Dover Publ., Mineola, N.Y., 2011
M. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University
Press, Cambridge, 2005
F.W.J. Olver, D.W. Lozier, C.W. Clark,R.F. Boisvert, Digital Library of Mathematical Functions,
National Institute of Standards and Technology, Gaithersburg, U.S.A., 2010 (http://dlmf.nist.gov)
I.N. Sneddon, Special Functions of Mathematical Physics and Chemistry, 3rd Edition, Longman,
London, 1980
G. Szego, Orthogonal Polynomials, 4th Ed., American Mathematical Society, Providence, RI, 1975
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
Total independent learning hours: 102
Total study hours: 150
Teaching methods will be a mix of lectures, examples classes and supervised problem solving
workshops, typically 36 lectures and 12 example classes/workshops (exact ratio may vary).
Lectures will contain an exposition of the module curriculum topics, and this theoretical material will
be illustrated with numerous theoretical and computational examples. These methods will be
supported by assessed problem sheets. The students will further have the opportunity to work on
assessed and non-assessed problems in the presence of the lecturer, who will be pro-actively
engaged in furthering their understanding of the material.
Subject specific learning outcomes 11(a)-(c) and generic learning outcome 12(b) will be addressed in
the lectures. Learning outcomes 11(c) and 12(a)-(d) will be addressed in the example classes as well
as in the written assignments.
16. Assessment methods and how these relate to testing achievement of the intended module
learning outcomes
Assessment: The module is assessed on the basis of examination (80%) and coursework (20%).
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UNIVERSITY OF KENT
Examination: A 2-hour written examination in Term 3 that consists of multi-part questions requiring a
mix of long and short answers to test the learning outcomes at varying levels of proficiency,
assessing the learning outcomes 11(a)-(c) and 12(b).
Coursework: This would normally consist of open-book assignments of unseen problems, assessing
the learning outcomes 12(a)-(d).
17. Implications for learning resources, including staff, library, IT and space
Staff: Convenor and moderator
Library: books are in the library or online
IT and Space: a suitable lecture room with good quality board space and data projection facilities
which can be used concurrently.
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/dyslexia support service, and specialist
support will be provided where needed.
19. Campus(es) 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"
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Director of Learning and Teaching/Director of
Graduate Studies (delete as applicable)
Date
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Print Name
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"
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Head of School
Date
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Print Name
Module Specification Template
Last updated February 2013
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