|
| Module Availability |
| Spring |
|
|
| Assessment Pattern |
|
Unit(s) of Assessment
|
Weighting Towards Module Mark( %)
|
|
Assignment
|
15
|
|
Class Test
|
10
|
|
Examination
|
75
|
|
Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass this module.
|
|
|
|
| Module Overview |
| The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. |
|
|
| Prerequisites/Co-requisites |
MAT1015 Calculus (MS114)
MAT1016 Linear Algebra (MS124)
MAT1017 Proof, Probabily and Experiment (MS125): Experiment submodule |
|
|
| Module Aims |
| The aim of this module is to study both qualitative and quantitative aspects of linear PDEs in one and two space dimensions. |
|
|
| Learning Outcomes |
By the end of the module, a student should be able to
- classify linear PDEs and choose the appropriate method to solve them;
- solve linear PDEs using the method of characteristics, Fourier transform, and separation of variables;
- interpret solutions;
- understand the use of the maximum principle and energy methods for uniqueness and well-posedness. |
|
|
| Module Content |
The contents of the module will include:
- Linear PDEs: Examples, classification of PDEs, their physical interpretation and derivation.
- First-order PDEs: Method of characteristics.
- Wave and heat equation in one space dimension: d’Alembert’s solution, energy methods, Fourier series, Fourier transform, and solution of boundary-value problems through separation of variables.
- Interpretation of solutions.
-
Laplace
’s equation: mean-value theorem, maximum principle, Poisson formula. |
|
|
| Methods of Teaching/Learning |
Teaching is by lectures, tutorials and example classes. Learning takes place through lectures, exercises (example sheets), preparation for tests and background reading.
There will be 3 contact hours for 10 weeks consisting of lectures, tutorials and example classes. |
|
|
| Selected Texts/Journals |
- P.V. O'Neil, Beginning Partial Differential Equations, John Wiley & Sons, (1999).
- W.A. Strauss, Partial Differential Equations, John Wiley & Sons, (1992).
|
|
|
| Last Updated |
| September 10 |
|
