Course syllabus for Differential equations

Course syllabus adopted 2026-02-19 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 74125
  • Maximum participants70
  • 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

In programmes

Examiner

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

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

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
  • analyze fixed points and local properties of autonomous dynamical systems
  • solve partial differential equations by the characteristic method and by separation of variables
  • solve numerically ordinary 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). Solvability of ODE. Initial value problem. Systems of ODE. Hamiltonian systems. Autonomous dynamical systems. Numerical methods including convergence and stability. Boundary value problem.

Partial differential equations (PDE). Classification of PDE. Linear first order PDE. Method of characteristics. Conservation laws. Heat equation, wave equation, Boundary value problem. Separation of variables and Fourier series, Examples of PDE from physics, among which Maxwell equations and Euler equations. 

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 about disability study support.