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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
MVE162 - Ordinary differential equations and mathematical modelling  
 
Syllabus adopted 2016-02-09 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

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0115 Written and oral assignments 0,0c Grading: UG   0,0c    
0215 Examination 7,5c Grading: TH   7,5c   29 May 2017 am H   03 Jan 2017 am SB   21 Aug 2017 pm SB  

In programs

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

Examiner:

Biträdande professor  Alexey Geynts


Replaces

MVE160   Mathematical modelling MVE161   Ordinary differential equations and mathematical modelling


  Go to Course Homepage

Eligibility:


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 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)

  • 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
  • write and work through a scientific text.

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.
The course also contains a part of scientific communication, focused on writing a scientific report. A student who has successfully completed a bachelor project is excempted from this part.

Organisation

Teaching includes two lectures and one exercise pass per week. Students are supposed to do two-three smaller mandatory modeling assignments. These will be done in working groups of 2-3 people. There will be a lecture and supervision for the scientific communication part.

Literature

Hartmut Logemann, Eugene P. Ryan
Ordinary Differential Equations Analysis, Qualitative Theory and Control Springer-Verlag London 2014

Examination

The examination consists of a written exam at the end of the course, and of both written reports on mandatory modeling assignments. Attendance at the scientific communication lecture is compulsory.


Page manager Published: Thu 04 Feb 2021.