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## Syllabus for

TMA013 - Ordinary differential equations

Syllabus adopted 2008-02-24 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

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 No Sp 0101 Examination 7,5c Grading: TH 7,5c Contact examiner, 27 Aug 2009 am V

#### In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR - Control specialization, Year 1 (elective)

#### Examiner:

Professor  Bernt Wennberg
Bitr professor  Hjalmar Rosengren

#### 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.

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

`After the course the students will:- know the  basic existence and uniqueness theorems for initial valueproblems- be able to solve linear systems using the complex exponential functions- be able to sketch and interpret phase portraits of two-dimensionalautonomous systems- be able to find equilibrium points of autonomous systems, and investigatetheir stability- be familiar with Green's functions and their application to boundary valueproblems- understand elementary numerical methods and be able to use numerical software`

#### Content

`Existence and uniqueness theorems. Solution of linear systems using thematrix exponential function. Phase portraits of autonomous systems.Investigation of equilibrium points by Liapunov's method and bylinearization. Solution of boundary value problems using Green's function.Brief introduction to mathematical software and numerical methods forordinary differential equations.`

#### Organisation

The course consists of lectures and exercise classes, and a guided computer session.

#### Literature

will be announced at the course web page

#### Examination

Written examination combined with a mandatory computer laboration

Page manager Published: Thu 04 Feb 2021.