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## Syllabus for

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 31 Aug 2007 am V

#### In programs

TTFYA ENGINEERING PHYSICS, Year 4 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TM Teknisk matematik, Year 2 (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: Thu 03 Nov 2022.