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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2016/2017

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Numerical Partial Differential Equations (MATH10044)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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.
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
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Differential Equations (MATH10066)
Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Academic year 2016/17, Available to all students (SV1) 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 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
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:
  1. Study solutions to partial differential equations using numerical methods
  2. Discretise partial differential equations via the finite difference method
  3. Discretise weak form partial differential equations via the finite element method
  4. Understand the principles of discretisation consistency, stability, and accuracy
Reading List
The suggested textbook for the course is "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J LeVeque.
Additional Information
Course URL https://info.maths.ed.ac.uk/teaching.html
Graduate Attributes and Skills Not entered
KeywordsNPDE
Contacts
Course organiserDr James Maddison
Tel: (0131 6)50 5036
Email: j.r.maddison@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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