Syllabus for |
|
| The course has been discontinued |
TMA632 - Partial differential equations, project course
|
| Partiella differentialekvationer, projektkurs |
| |
| Syllabus adopted 2019-02-22 by Head of Programme (or corresponding) |
| Owner: MPENM |
|
|
7,5 Credits
|
| Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail |
| Education cycle: Second-cycle |
|
Major subject: Mathematics
|
|
Department: 11 - MATHEMATICAL SCIENCES
|
Teaching language: English
Application code: 20113
Open for exchange students: Yes
| Module |
|
Credit distribution |
|
Examination dates |
|
Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0101 |
Examination |
7,5 c |
Grading: TH |
|
|
7,5 c
|
|
|
|
|
|
|
In programs
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
Examiner:
Anders Logg
Go to Course Homepage
Eligibility
General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Partial differential equations - first course or equivalent knowledge.
Aim
The course aims at giving a solid introduction to modern theoretical and computational methods for ordinary differential equations (ODE) and partial differential equations (PDE) with training both in theoretical modeling and computational simulations.
Learning outcomes (after completion of the course the student should be able to)
- use and (to some extent) develop software for solving numerically a choice of ODE and PDE.
- in a written report document the model description, the mathematical theory, the numerical models/algorithms, error analysis and numerical examples.
- make an oral presentation of a theoretical and computational investigation.
Content
Duality and adjoint operators. Stability and duality based a posteriori error analysis for ODE. Stability and duality based a posteriori error analysis for PDE. Adaptivity. Computational methods for various types of PDE such as diffusion, convection-diffusion, reaction-diffusion, wave propagation, fluid flow, electromagnetics, and fluid-structure interaction.
Organisation
Some introductory lectures and supervision of projects.
Literature
Computational Differential Equations, K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Studentlitteratur/Cambridge University Press, 1996.
MATLAB, Octave, Puffin/Dolfin (www.bodysoulmath.org), COMSOL MultiPhysics.
Examination including compulsory elements
Two compulsory projects. Oral and written presentations of the projects.