Course syllabus for Partial differential equations - second course

The course syllabus contains changes
See changes

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish namePartiella differentialekvationer fortsättningskurs
  • CodeTMA026
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 20119
  • Open for exchange studentsYes

Credit distribution

0101 Examination 7.5 c
Grading: TH		 7.5 c
  • 31 Maj 2022 am J
  • Contact examiner
  • 18 Aug 2022 am J

In programmes

Examiner

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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.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

The course syllabus contains changes

  • Changes to examination:
    • 2022-04-23: Exam date Exam date changed by Elisabeth Eriksson
      [33893, 55914, 3], New exam for academic_year 2021/2022, ordinal 3 (not discontinued course)