Course syllabus for Partial differential equations

Course syllabus adopted 2021-01-15 by Head of Programme (or corresponding).

Overview

  • Swedish namePartiella differentialekvationer
  • CodeTMA690
  • Credits4.5 Credits
  • OwnerTKTFY
  • Education cycleFirst-cycle
  • Main field of studyMathematics, Engineering Physics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 57118
  • Maximum participants60
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0194 Examination 4.5 c
Grading: TH		 4.5 c
  • 12 Jan 2023 am J
  • 05 Apr 2023 am J
  • 14 Aug 2023 pm J

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first 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

The same as for the programme that owns the course.
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

Real analysis, Multivariabel analysis, Fourier analysis.

Aim

Partial differential equations are powerful computational tools in science and technology with an manifold of applications. This motivates to have a separate course in partial differential equations at the Engineering physics programme.

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

The student should be able to show a basic understanding of
the fundamental types of partial differential equations,
and the basics of distribution theory.
The student should be able to give variational formulations
of boundary value problems and to use the finite element method for
solving such numerically.
The student should be able to solve initial value problems using
Fourier analysis and eigenfunctions.
The student should be able to use fundamental solutions, Green's
formulas and Green's functions.

Content

Systems av ordinary differential equations.
Change of variables for first order partial differential equations.
Heat, wave and Laplace's equations.
Linear PDE problems.
Introduction to distribution theory.
Variational methods for boundary value problems. The Sobolev space and Lax-Milgram's theorem.
Introduction to the finite element method.
Fourier transformation of tempered distributions, for solving inital value problems.
Qualitative analysis of solutions.
Harmonic functions, Green's functions, mean value theorems and maximum principles.
Laplace eigenfunctions and eigenvalues, for solving initial/boundary value problems.
Classification of second order PDEs.
Examples of systems of first order PDEs and of non-linear PDEs.

Organisation

Lectures, problems solving sessions and a compulsary computer project about FEM.

Literature

Rosén, Andreas: Partial differential equations, weak derivatives and systems of ODEs.
Strauss, Walter A.: Partial differential equations. An Introduction. Second edition, 2007.

Examination including compulsory elements

A compulsary computer project and a written exam.

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.