Undergraduate Course: Numerical Partial Differential Equations (MATH10044)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This course introduces the numerical discretisation of partial differential equations. A number of different partial differential equations will be considered, and methods for yielding approximate numerical solutions will be studied. The course makes significant use of tools from linear algebra. The assessment is 80% examination and 20% coursework. The coursework includes the use of MATLAB.
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| Course description |
The numerical solution of partial differential equations plays a central role in many areas of modern science. This course will introduce the fundamental concepts and methods of numerical partial differential equations. The methods are built up by considering discretisations of prototypical equations: the Poisson equation, diffusion equation, and advection equation. The course will begin with a study of classic finite difference techniques, and will later move on to a consideration of weak form partial differential equations and the finite element method.
Syllabus:
1. Finite difference discretisation
2. The method of lines
3. Consistency, stability, and convergence
4. Methods for proving numerical stability
5. Galerkin finite element discretisation
6. Boundary conditions
7. Discretisation matrices
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Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2015/16, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework 20%, Examination 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
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| Main Exam Diet S2 (April/May) | Numerical Partial Differential Equations (MATH10044) | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Study solutions to partial differential equations using numerical methods
- Discretise partial differential equations via the finite difference method
- Discretise weak form partial differential equations via the finite element method
- Understand the principles of discretisation consistency, stability, and accuracy
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Reading List
| The suggested textbook for the course is "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J LeVeque. |
Contacts
| Course organiser | Dr James Maddison
Tel: (0131 6)50 5036
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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