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Syllabus for

Academic year
TMA026 - Partial differential equations - second course  
 
Syllabus adopted 2012-02-22 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5c Grading: TH   7,5c   31 May 2016 am M   Contact examiner,  26 Aug 2016 am M  

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)

Examiner:

Professor  Axel Målqvist



  Go to Course Homepage

Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

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 difference and finite element methods for these problems.
- understand 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 linear ordinary differential equations and linear elliptic, parabolic and hyperbolic partial differential equations. The maximum principle. Finite element and finite difference methods. Error estimates. Applications to heat conduction, wave propagation, convection-diffusion, reaction-diffusion, and elasticity.

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

Written exam and exercises handed in.


Page manager Published: Mon 28 Nov 2016.