Course syllabus for Partial differential equations, first course

Course syllabus adopted 2023-02-14 by Head of Programme (or corresponding).

Overview

  • Swedish namePartiella differentialekvationer, grundkurs
  • CodeTMA373
  • 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 20137
  • Open for exchange studentsYes

Credit distribution

0122 Laboratory, part A 1.5 c
Grading: UG		0 c0 c1.5 c0 c0 c0 c
0222 Examination, part B 6 c
Grading: TH		0 c0 c6 c0 c0 c0 c

In programmes

Examiner

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

Linear algebra and calculus in one and several variables

Aim

The course gives an introduction to the modern theory of partial differential equations (PDE) with applications in science and engineering. It also presents an introduction to the finite element method (FEM) as a general tool for numerical solution of PDE. The students will obtain a basic understanding of qualitative properties, such as existence, regularity, uniqueness, and stability of solutions of PDE and their approximations by means of FEM. The understanding should be sufficient to allow them, in a future professional or research situation, to model scientific problems as PDE and to construct and analyze numerical approximation methods.   

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

  • derive weak formulations of classical PDEs.
  • derive stability estimates for classical PDEs.
  • derive and apply classical numerical methods for IVPs.
  • formulate Galerkin finite element methods for PDEs. 
  • derive (a priori and a posteriori) error estimates.
  • implement FEM in 1D and 2D.
  • understand the concept of adaptivity.

Content

  • Strong and weak solutions to elliptic, parabolic, and hyperbolic partial differential equations (PDE).
  • Lax-Milgram theorem.
  • Finite element methods (FEM) for BVP and PDE
  • Error analysis of the FEM.
  • Numerical methods for IVP.
  • FEM for PDEs in 2D.
  • Error analysis in 2D.

    Organisation

    Lectures (about 35 hours), exercises (about 21 hours) and home assignments (consisting of both theoretical and computer labs).

    Literature

    References and supplementary course material are posted on the course webpage.

    Examination including compulsory elements

    Written exam, and pass on computer labs.

    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.