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Syllabus for

Academic year
TMA026 - Partial differential equations - second course
Partiella differentialekvationer fortsättningskurs
 
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: 20124
Open for exchange students: Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5c Grading: TH   7,5c   Contact examiner

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPNAT NANOTECHNOLOGY, MSC PROGR, Year 1 (compulsory elective)

Examiner:

Axel Målqvist


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

The students should have basic knowledge about Fourier series and the Fourier transform. Basic knowledge about partial differential equations (for instance "Partial Differential Equations - first course") and functional analysis is also recommended but not necessary.

Aim

The course is a complement to the introductory course "Partial Differential Equations - first course" and presents a more theoretical foundation for linear partial differential equations and numerical methods.

Learning outcomes (after completion of the course the student should be able to)

- formulate models in science and engineering that involve partial differential equations including the correct boundary conditions and initial conditions.
- prove various types of existence, stability and regularity results for these problems.
- formulate finite element methods for these problems.
- explain the role of stability in the error analysis of such methods and be able to prove error estimates.

Content

Existence and regularity of solutions of elliptic, parabolic and hyperbolic partial differential equations. The maximum principle. The Finite element method. Error estimates. Applications to heat conduction, wave propagation, eigenvalue problems, convection-diffusion, and reaction-diffusion.

Organisation

Lectures and exercise classes.

Literature

S. Larsson and V. Thomée, Partial Differential Equations with Numerical Methods, Texts in Applied Mathematics 45, Springer, 2003.

Examination including compulsory elements

Written exam and exercises handed in.


Published: Mon 28 Nov 2016.