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Syllabus for

Academic year
MVE161 - Ordinary differential equations and mathematical modelling
 
Syllabus adopted 2013-02-21 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
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students
Block schedule: X

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0113 Examination 7,5c Grading: TH   7,5c   02 Jun 2014 am V,  25 Aug 2014 pm V

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (elective)
TKTEM ENGINEERING MATHEMATICS, Year 2 (compulsory)

Examiner:

Biträdande professor  Alexey Geynts


Replaces

MVE160   Mathematical modelling

Course evaluation:

http://document.chalmers.se/doc/8b7d07fc-3f92-41eb-bb0e-5bb5bc91a5af


  Go to Course Homepage

Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

The prerequisites for the course are the equivalent of 60 higher education credits in Mathematics, including multivariable analysis, linear algebra and a course in programming.

Aim

Students will be able to use general theory for ordinary differential equations (ODE) and apply the theory and computers to formulate and to solve modeling problems.

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

After completing the course, the student will be able to
* describe and explain the main concepts and theories for ODEs covered in the course
* formulate mathematical models in terms of ODE
* make analytical analysis of models formulated in terms of ODE
* make numerical analysis of a mathematical model and to implement it in Matlab
* interpret the results of a mathematical model.

Content

General theory for ordinary differential equations (ODE) such as existence and uniqueness of solutions to ODE, theory of linear systems of ODE, and stability properties of nonlinear ODE using Lyapunovs functions.

Examples of mathematical modeling in physics, chemistry and environment.

Organisation

Teaching includes two lectures and one exercise pass per week. Students are supposed to do two smaller mandatory modeling assignments. These will be done in working groups of 2-3 people.

Literature

Gerald Teschl. Ordinary Differential Equations and Dynamical Systems. Graduate Studies in Mathematics, Volume 140, Amer. Math. Soc., Providence, 2012. (available free on the authors homepage)

Examination

The examination consists of a written exam at the end of the course, and of both written reports and oral presentations of mandatory modeling assignments.


Published: Mon 28 Nov 2016.