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Syllabus for

Academic year
TMA026 - Partial differential equations - advanced course
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0101 Examination 5,0 c Grading: TH   5,0 c    

In programs

TM Teknisk matematik, Year 2 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)

Examiner:

Professor  Stig Larsson



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

The students should have basic knowledge about Fourier series and the Fourier transform. Some basic knowledge about partial differential equations and functional analysis is also recommended but not necessary.

Aim

Existence and regularity of solutions of linear ordi-nary differential equations and linear elliptic, para-bolic 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, neutron transport.

Content

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

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: Thu 03 Nov 2022.