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Syllabus for

Academic year
TMA013 - Ordinary differential equations
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0101 Examination 5,0 c Grading: TH   5,0 c   Contact examiner

In programs

TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TM Teknisk matematik, Year 2 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)

Examiner:

Docent  Johannes Brasche



Eligibility:

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

Aim

Ordinary differential equations (ODE) are used in modelling a wide variety of phenomena in engineering and sciences. An introduction to the theory of linear and non - linear ODEs will be given and, in particular, existence, uniqueness and stability of solutions will be discussed. Quite often the mathe-matical model is so complex that it cannot be solved in closed form.
For this reason one wants to find approximative solutions. The corresponding algorithms have to be efficient and safe. In the course also algorithms for the numerical solution of ODEs will be presented and a theoretical analysis of these algorithms will be done.

Content

Initial value problems. Existence, uniqueness and stability. Runge - Kutta methods, stability, conver-gence, error estimates, multistep methods. Adaptivity.

Literature

U.M.Ascher, L.R.Petzold: Computer Methods for Ordinary Differential Equations and Differential - Algebraic Equations, SIAM, 1998.

Examination

Written examination combined with homework partially based on computer computations.


Page manager Published: Mon 28 Nov 2016.