UNIVERSITY OF KENT
MODULE SPECIFICATION
SECTION 1: MODULE SPECIFICATIONS
1.
Title of the module: Mathematical Techniques and Differential Equations (MA588)
2.
School or partner institution which will be responsible for management of the
module: School of Mathematics, Statistics & Actuarial Science
3.
Start date of the module: existing module (revised version start date September 2014)
4.
The number of students expected to take the module: 150
5.
Modules to be withdrawn on the introduction of this proposed module and
consultation with other relevant Schools and Faculties regarding the withdrawal:
N/A
6.
The level of the module: I
7.
The number of credits and the ECTS value which the module represents: 15 credits
(ECTS 7.5)
8.
Which term(s) the module is to be taught in (or other teaching pattern): Spring
9.
Prerequisite and co-requisite modules: MA321 (Calculus and Mathematical
Modelling), MA322 (Proofs and Number), MA323 (Matrices and Probability) or MA326
(Matrices and Computing)
10. The programme(s) of study to which the module contributes: Mathematics,
Mathematics & Statistics, Mathematics with Foundation Year, Financial Mathematics,
Mathematics and Accounting & Finance, Mathematics & Management Science,
Mathematics & Computer Science.
11. The intended subject specific learning outcomes
On successful completion of the module students will:
11.1 be able to solve linear ordinary differential equations by series;
11.2 understand the concept of the Fourier series expansion of a function;
11.3 be able to solve partial differential equations by separation of variables;
11.4 understand how Fourier series and special functions arise in the solution of
boundary and initial value problems in applied mathematics and mathematical physics;
11.5 appreciate the uses of Fourier transforms and be able to calculate them for simple
functions;
11.6 appreciate the mathematical and physical aspects of the solutions of the equations
considered, as well as their computation with MAPLE.
12. The intended generic learning outcomes
On successful completion of the Module, students will have developed:
12.1 an analytical approach to solving problems in applied mathematics and physics
involving ordinary and partial differential equations;
12.2 their ability to communicate these solutions and calculations;
12.3 their numeracy and computational skills;
12.4 their ability to plan and carry out effective ways of studying;
12.5 their key skills in numeracy, problem solving and computing.
13. A synopsis of the curriculum: Lecture syllabus: 36 Lectures (Term 1)
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UNIVERSITY OF KENT
Series Solutions of Linear Ordinary Differential Equations: Introduction and solution
of first/second order equation at regular points, and regular singular points: Frobenius'
method. Application to Legendre's equation and polynomial solutions, Bessel's equation,
etc. Method of reduction in order.
Orthogonal Polynomials and Functions: Defining property: inner products for
functions. Generating functions, recurrence relations and Rodrigues formula for
Legendre and Hermite polynomials; other examples (e.g. Chebyshev, Laguerre) where
appropriate.
Fourier Series: Periodic functions and their Fourier series. Sufficient conditions for
convergence. Fourier sine/cosine series, and complex Fourier series. Differentiation of
Fourier series. Parseval's theorem. Generalized Fourier series.
Partial Differential Equations: Linear second order equations: Laplace's equation,
diffusion equation, wave equation, Schrodinger's equation. Separation of variables in
Cartesian and polar coordinate systems. Use of Fourier series and special functions to
solve these equations with given initial and boundary conditions.
Fourier Transforms: Basic properties and transforms of simple functions, and physical
applications. Parseval's theorem
14. Indicative Reading List.
E Kreyszig, Advanced Engineering Mathematics, Wiley
CR Wylie and LC Barrett, Advanced Engineering Mathematics, McGraw-Hill
RK Nagle and EB Saff, Fundamentals of Differential Equations, Benjamin
IN Sneddon, Fourier series, Routledge
R Haberman, Elementary applied partial differential equations: with Fourier series and
boundary value problems, Prentice-Hall
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 learning outcomes
The module will consist of 36 hours of lectures, 12 hours of classes which will consist
of problem-solving sessions and MAPLE workshops, 102 hours of private study. Total
Study hours: 150.
The lectures will contain a description of the techniques concerned along with proofs of
some of their general properties (as described in 11.1-11.6). To illustrate this material,
worked examples of particular methods (as described in 11.1-11.6) will also be provided
in lectures, and these will be reinforced by the assessed problem sheets and MAPLE
worksheets. The problem-solving sessions provide an environment for the students to
tackle the assessed questions and other non-assessed model problems (as described in
11.1-11.6), with the aid of the lecturer where necessary. At the same time these
sessions should be a forum for the students to raise questions if they have had particular
difficulties with the lecture material. These classes are complemented by the MAPLE
workshops where the students tackle (unassessed) worksheets containing MAPLE code
to illustrate theory and examples discussed in the lectures. This means that they learn
an alternative computer-based approach to solving problems and visualizing the
solutions. The assessed work is marked to provide feedback on the correctness of
calculation and presentation of answers interpreted via the theory from lectures. These
teaching methods will aid students to develop generic learning outcomes 12.1-12.5.
16. Assessment methods and how these relate to testing achievement of the intended
learning outcomes: The unit is assessed by examination (80%) and by coursework
assessment (20%).
Coursework Assessment: This will consist of open-book written assessments which
are completed by students, partly during problem classes but mostly outside contact
hours.These consist of questions and numerical problems requiring short and long
answers and they test the learning outcomes 11.1-11.6 and 12.1-12.5
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UNIVERSITY OF KENT
Examination: A 2-hour written examination in Term 3 that will consist of questions and
numerical problems requiring short and long answers which test the learning outcomes
outlined in 11.1-11.6 and 12.1-12.5.
17. Implications for learning resources, including staff, library, IT and space: None
(existing module).
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
…………………………………………………
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
…………………………………………………….
Print Name
SECTION 3: MODULE IS PART OF A PROGRAMME IN A PARTNER COLLEGE OR
VALIDATED INSTITUTION
(Where the module is proposed by a Partner College/Validated Institution)
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UNIVERSITY OF KENT
Statement by the Nominated Officer of the College/Validated Institution (delete as
applicable): "I confirm that the College/Validated Institution (delete as applicable) has
approved the introduction of the module and will be responsible for its resourcing"
.................................................................
Nominated Responsible Officer
College/Validated Institution
of
..............................................
Partner
………………………………………………….
Print Name
…………………………………………………..
Post
………………………………………….
Partner College/Validated Institution
Module Specification Template
Last updated October 2012
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Date