Syllabus for |
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| TMA026 - Partial differential equations - second course |
| Partiella differentialekvationer fortsättningskurs |
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| Syllabus adopted 2019-02-22 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits
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| Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail |
| Education cycle: Second-cycle |
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Major subject: Mathematics |
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
Application code: 20124
Open for exchange students: Yes
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0101 |
Examination |
7,5c |
Grading: TH |
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7,5c
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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.