Course syllabus for Ordinary differential equations and mathematical modelling

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameOrdinära differentialekvationer och matematisk modellering
  • CodeMVE162
  • Credits7.5 Credits
  • OwnerTKTEM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 59113
  • Open for exchange studentsYes

Credit distribution

0115 Written and oral assignments 0 c
Grading: UG		 0 c
0215 Examination 7.5 c
Grading: TH		 7.5 c

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second 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

English 6 (or by other approved means with the equivalent proficiency level)
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

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 including compulsory elements

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.

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.