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]
|
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 44,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
54 )
|
| Assessment (Further Info) |
Written Exam
70 %,
Coursework
30 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Written Exam %: 70
Practical Exam %: 0
Coursework %: 30 |
| 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 |
Minutes |
|
| Main Exam Diet S2 (April/May) | Partial Differential Equations 3 | 120 | | | Resit Exam Diet (August) | Partial Differential Equations 3 | 120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Distinguish between the three different types of second order partial differential equations; this includes their properties and general solution behaviour
- Calculate the analytical solution of engineering problems described by the three types of linear, constant coefficient second order partial differential equationsÂ
- Use Python to simulate the numerical solution of engineering problems described by second order partial differential equations
- Evaluate the performance and suitability of the numerical methods for the three different types of partial differential equations
|
Reading List
Applied partial differential equations
Glyn James: Advanced Modern Engineering Mathematics, Chapter 9, required from Engineering Mathematics 2
Svein Linge, Hans Petter Langtangen: Programming for Computations - Python A Gentle Introduction to Numerical Simulations with Python 3.6, Springer, 2020
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 Martin Sweatman
Tel: (0131 6)51 3573
Email: |
Course secretary | Mrs Marian Conlan
Tel:
Email: |
|
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