Course syllabus for Differential equations

Course syllabus adopted 2023-02-05 by Head of Programme (or corresponding).

Overview

  • Swedish nameDifferentialekvationer
  • CodeMVE680
  • Credits7.5 Credits
  • OwnerTKGBS
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 74118
  • Maximum participants70
  • Block schedule
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0122 Examination 7.5 c
Grading: TH		 7.5 c
  • 13 Jan 2024 pm J
  • 03 Apr 2024 pm J
  • 29 Aug 2024 am 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

Multivariable analysis, Linear algebra, a course in programming

Aim

The course deals with the mathematical theory for ordinary and partial differential equations and how these are solved numerically.

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

  • investigate the solvability of differential equations with analytical methods
  • analyse fixed points and local properties of autonomous dynamical systems
  • derive the weak formulation of partial differential equations
  • solve numerically ordinary and partial differential equations
  • carry out a stability and error analysis of numerical methods
  • combine knowledge of different concepts in practical problem solving

Content

Ordinary differential equations (ODE). Systems of ODE. Autonomous dynamical systems.
Solvability of ODE. Numerical methods including convergence and stability. Boundary value problem.

Partial differential equations (PDE). Classification of PDE. Linear first order PDE. Conservation laws. Burger equation. Heat equation, wave equation, Laplace equation. Exempel of PDE from physics, among which Maxwell equations and Euler equations. Boundary value problem. Weak formulation of PDE. Numerical methods. Introduction to the finite difference and finite element method.

Organisation

Lectures and exercises 

Literature

The literature will be posted on the course homepage before the course starts. 

Examination including compulsory elements

Written exam. Voluntary numerical projects giving bonus points for the exam may be given.   

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.