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Syllabus for

Academic year
TMA014 - Ordinary differential equations and dynamical systems
Syllabus adopted 2014-02-13 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mathematics

Teaching language: English
Open for exchange students

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0110 Examination 7,5 c Grading: TH   7,5 c    
0210 Laboratory 0,0 c Grading: UG   0,0 c    

In programs



Docent  Michael Björklund


TMA013   Ordinary differential equations

  Go to Course Homepage


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

The equivalent of  60 higher education credits in Mathematics, including courses in  multivariable analysis and linear algebra.


The purpose of the course is to give an introduction to the basic
theory of ordinary differential equations, in particular the initial
value problem: existence and uniqueness theorems, stability
analysis. Morover, the course gives an introduction to the theory of
dynamical systems, discrete as well as continuous. The course also
introduces some numerical methods for studying dynamical systems and odes.

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

 - know the basic existence and uniqueness theorems for initial value problems
 - be able to solve linear systems using the complex exponential functions
 - know the definitions of diffeomorphisms and flows, and their
   interpretations as dynamical systems
 - be able to sketch and interpret phase portraits of two-dimensional
   autonomous systems
 - be able to analyse fixed points  and local properties of dynamical systems
 - be familiar with the basic terminology of dynamical systems


Existence and uniqueness theorems for ordinary differential
equations. Solution of linear systems using the matrix exponential
function. Basic theory of discrete and continuous dynamical systems,
properties of diffeomorphisms and flows.


The course is based on lectures where the theory is presented, and on
problem  classes. The students are expeceted to participate by
presenting their solutions to selected problems. There is also a
mandatory computer assignment.


The course literature will be announcedo in the course web page


The course assessment is based on a written exam and the written
report from the computer assignment. Active participation in the
problem classes is accounted for when setting grades 4  or 5, but not
required for grade 3 (pass).

Page manager Published: Mon 28 Nov 2016.