Syllabus for |
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| TMA013 - Ordinary differential equations |
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| Syllabus adopted 2009-02-26 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| Education cycle: Second-cycle |
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Major subject: Mathematics
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
| Course module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
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| 0101 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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11 Mar 2010 am V, |
19 Aug 2010 am V, |
15 Jan 2010 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
Go to Course Homepage
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 value
problems
- be able to solve linear systems using the complex exponential functions
- be able to sketch and interpret phase portraits of two-dimensional
autonomous systems
- be able to find equilibrium points of autonomous systems, and investigate
their stability
- be familiar with Green's functions and their application to boundary value
problems
- understand elementary numerical methods and be able to use numerical software
Content
Existence and uniqueness theorems. Solution of linear systems using the
matrix exponential function. Phase portraits of autonomous systems.
Investigation of equilibrium points by Liapunov's method and by
linearization. Solution of boundary value problems using Green's function.
Brief introduction to mathematical software and numerical methods for
ordinary 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