Undergraduate Course: Partial Differential Equations 3 (SCEE09004)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 9 (Year 3 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Most physical problems in science and engineering depend on changes in multiple dimensions and these problems are described by Partial Differential Equations (PDE). These equations contain 2 or more partial derivatives, for example a time and a space dimension or multiple space dimensions.This course introduces first and second order PDEs and the solution properties for different classes of PDEs. Based on these different solution properties, we will develop analytical and numerical solution methods for the different classes of PDEs. |
| Course description |
The course will consist of 20 lectures and 10 tutorial/lab sessions.
Lectures:
1.Introduction to and classification of partial differential equations (PDEs) [2 lectures]
2.Analytical solution of the Laplace, heat and wave equation: separation of variables, Laplace transform method, d¿Alembert and characteristics [8 lectures]
3.Introduction to numerical methods for PDEs [2 lectures]
4.Application of the finite difference method to the different types of PDEs: boundary value problems for stationary PDEs, initial-boundary value problems for transient PDEs, handling of different boundary conditions, accuracy and stability of the solutions [8 lectures]
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Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2017/18, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 20,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 10,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
56 )
|
| Assessment (Further Info) |
Written Exam
60 %,
Coursework
40 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Written Exam %: 60«br /»
Practical Exam %: 0«br /»
Coursework %: 40«br /»
«br /»
The coursework consists of two individual assignments. The first shorter assignment [20%] will focus on the analytical solution of PDEs. The second assignment [20%] will focus on the numerical solution; here the students will be required to develop a numerical solution to a given problem and to analyse the system behaviour. Students will submit a short report as well as the Matlab code for this assignment. |
| Feedback |
The tutorial/lab sessions provide opportunities for formative feedback and the two coursework assignments will provide summative feedback. |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | | 2:00 | | | Resit Exam Diet (August) | | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- A sound basis in partial differential equations to give students an understanding of the properties of partial differential equations and their solutions;
- Practice in applying analytical methods for the solution of partial differential equations;
- Basic understanding of the workings and limitations of numerical methods for the solution of partial differential equations;
- Practice in the numerical solution of the three different types of partial differential equations using Matlab.
|
Reading List
Applied partial differential equations
Glyn James: Advanced Modern Engineering Mathematics, Chapter 9¿required from Engineering Mathematics 2
Randall J. LeVeque: Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems, SIAM, 2007¿available online
Herve Le Dret, Brigitte Lucquin: Partial Differential Equations: Modeling, Analysis and Numerical Approximation, Springer, 2016¿available online
S.C. Chapra, R.P Canale: Numerical Methods for Engineers, 6th edition, McGraw-Hill, 2010
Andrew R. Mitchell, David F. Griffiths: The finite difference method in partial differential equations, Wiley, 1980
Leon Lapidus, George F. Pinder: Numerical Solution of Partial Differential Equations in Science and Engineering
Joel Chaskalovic: Mathematical and Numerical Methods for Partial Differential Equations
Mathematical theory of partial differential equations
Qing Han, A Basic Course in Partial Differential Equations
Lawrence C. Evans: Partial Differential Equations
Numerical methods
William H. Press:Numerical Recipes in C: The Art of Scientific Computing |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Partial Differential Equations,Mathematical Modelling,Mathematical Methods,Mechanical Engineering |
Contacts
| Course organiser | Dr Daniel Friedrich
Tel: (0131 6)50 5662
Email: |
Course secretary | Mrs Lynn Hughieson
Tel: (0131 6)50 5687
Email: |
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