Download EMPS - Module - MAS2016 Methods for Differential Equations

EMPS - Module - MAS2016 Methods for Differential Equations.rtf
MODULE CODE
MAS2016
MODULE LEVEL
2
MODULE TITLE
Methods for Differential Equations
LECTURERS
Prof Andrew Soward (Coordinator),
CREDIT VALUE
15
ECTS VALUE
7.5
PRE-REQUISITES
MAS2001 (or equivalent)
CO-REQUISITES
DURATION OF MODULE
1 semester(2)
TOTAL STUDENT STUDY TIME
Overall, the module is expected to involve students in
approximately 150 hours of learning, including formal contact,
personal study, coursework and assessment. The total formal
contact is 30 hours of lectures and 3 hours of examples classes.
AIMS
The main focus of this module is on differential equations and their solution, particularly partial differential equations. These
techniques are used extensively in subsequent modules in Applied Mathematics, for example in Hydrodynamics and Quantum
theory.
Topics covered include: Second order ordinary differential equations; Method of Frobenius and Variation of Parameters;
Special functions, with emphasis on Legendre polynomials and their application to the solution of partial differential
equations. Many worked examples are provided.
AIMS.
The main aim of this module is the study of differential equations and their solution, particularly partial differential equations.
INTENDED LEARNING OUTCOMES
1. Module specific skills.
By the end of the module, students will:
(a) have a basic working knowledge of mathematical methods required to solve a wide range of problems in both science and
engineering.
2. Discipline specific skills.
The material provides the basic tools required in the advanced applications, particularly those subjects involving fluid
mechanics, quantum theory and mathematical biology.
3. Personal and key skills.
By the end of this module, students will have:
(b) an opportunity to develop their abilities, to monitor their own progress, to manage time, and to formulate and solve
complex problems.
LEARNING / TEACHING METHODS
Three lectures per week, some used as example classes.
ASSIGNMENTS
Regular example sheets.
ASSESSMENT
Examination (75%) 2 hour, closed book examination paper in May/June.
Coursework (25%) Regular example sheets.
SYLLABUS PLAN
Review of methods of solving linear first order differential equations. The general linear second order differential equation.
Reduction of order. Method of variation of parameters. Method of Frobenius, (8 lectures).
Last Revised:
EMPS - Module - MAS2016 Methods for Differential Equations.rtf
Orthogonal functions including Legendre and trigonometric functions. Further examples of special functions (e.g. Hermite
polynomials, Laguerre Functions, Chebyschev polynomials), (8 lectures).
Application of special functions to the solution of Laplace's equation, the diffusion equation and the wave equation by the
method of separation of variables. Normal modes. Series expansions of solutions. Applications to boundary value problems.
Waves in strings, (9 lectures).
Laplace transform: basic properties and evaluation; inverse Laplace transform and convolution. Dirac delta and Heaviside
functions. Fourier transform: basic properties and evaluation; inverse Fourier transform and convolution; Parseval's theorem.
Fourier Sine and Cosine transforms. Applications of Laplace and Fourier transforms to ordinary and partial differential
equations and boundary value problems, (8 lectures).
INDICATIVE BASIC READING LIST
Arfken G.B. & Weber H.J. "Mathematical Methods for Physicists" 5th, Harcourt/ Academic Press (2001), ISBN:
000-0-120-59825-6 (set)
Kreyszig E "Advanced Engineering Mathematics" 9th, Wiley (2006), ISBN: 978-0471728979 (set)
O'Neil P.V. "Advanced Engineering Mathematics" 2nd, Wadsworth (1987), ISBN: 000-0-534-06792-1 (set)
Stephenson G. & Radmore P.M. "Advanced mathematical methods for engineering and science students" , Cambridge
University Press (1990), ISBN: 000-0-521-36860-X (
EXTENDED READING LIST
DETAILED LEARNING OUTCOMES
DATE OF LAST REVISION
Last Revised: