Course PM
MAN460 - Ordinära differentialekvationer
Ordinary differential equations
The course deals wih
- theoretical aspects of ode's
    (existence and uniqueness of
solutions to the initial value problem;
    theory of linear systems;
    qualitative properties of solutions;
    stability of solutions;
    two-point boundary value problems and
Sturm-Liouville theory)
- practical use of ode's (mathematical models)
- a little about numerical methods (with a project)
The official course description (in swedish) can be found
here .
The schedule, with information about lecture rooms, can be
found
here .
(Note that all lectures in the afternoon, except the one on March
28, begin 15 minutes past the hour, while the morning lectures begin
on the hour).
A course diary, with information about the course activity so
far can be found
here .
Links to downloadable material are put
at the bottom of the page.
MAN460 is also an elective course in the international master's
programme "Engineering Mathematics", and hence it will be
given in English, if any one student prefers this.
NEWS AND IMPORTANT INFORMATION
- The exam from June 3 is now marked. Please contact me
if you wish to see it. I would also like to remind you to
hand in the lab reports.
- The second possibility for examination of this course
is
25th August 8.30 - 13.30
- Course evaluation
I have forgotten to organise an evaluation committee for the
course. Perhaps this is less important for a small course
like this one, but a course evaluation is still very
important of course. Please find here a
questionnaire with some
questions about the course. I would be very grateful if you
would like to hand in that to me, at the latest togehter
with the lab. To keep it anonymous, please put it in an
envelope (then you have to trust that I don't keep track of
who wrote it ...)
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A preliminary programme
Please return frequently to this page!
week day |
plan |
Comments and suggested problems |
w. 13 |
- Introduction to the course
- First order scalar equations, separable equations,
other special cases ...
- The initial value problem (existence and uniqueness
with a Lipschitz condition)
|
w. 14 |
- More theory: maximal solutions etc,
- Something about numerical methods, and introduction to
the lab
|
1, 2a, 4a, 5, 6 (note: (a) and (b) belong
to a separate question ...), 8, 13, 14, 16 (refers to
"another set of exercises) |
w. 15 |
Easter break
|
w. 16 |
Exam period
|
w. 17 |
- Linear systems
- Gronwall estimates, non-homogeneous equations
|
w. 18 |
- Linear systems with constant coefficients
- More linear algebra, the Cayley-Hamilton theorem etc.
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Recommended exercises (from first collection): 5,7,9,11,13,15
|
w. 19 |
- Stability
- Liapunov functions etc.
- Phase portraits
|
w. 20 |
- More on dynamical systems
- Peano's existence theorem
|
w. 21 |
- Two point boundary value problems
- Sturm Liouville theory
|
w. 22 |
- Orthogonal systems
- Self adjoint operators
|
3/6 |
Written exam
|
16/6 |
Last day to hand in lab report
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Course litterature
- Walter, Wolfgang: Ordinary
Differential Equations , Springer (1998).
Can be orderd e.g. at
adlibris.se . It is also sold at Cremona.
-This book will be the base for the course at least this
year.
- Andersson, K.G., Böiers, L.-C.:
Ordinära differentialekvationer ,
Studentlitteratur (1992).
Can be orderd e.g. at
adlibris.se , and it is also available at Cremona.
- This book used to be the standard book for the course,
and it is very well adapted to the course
programme. Unfortunately it is not available in
English. However, for anyone who understands Swedish, this
is quite sufficient as course litterature.
- Simmons, G.F.: Differential
equations with applications and historical notes
McGraw-Hill. Can be orderd e.g. at
adlibris.se
- A nice book on ordinary differential equations, which
also contains many good exercises (some will be presented
in the course). It also presents some of the men who
created the theory (of course, also women have made very
important contributions to this theory, but Simmons has
chosen only men in his list)
-
Some additional
material, will be available for download from the
webpage:
- Instructions for the computer lab project
here
- Some exersices (mostly taken from Walter) can be
found here
- Another set of exersices
here
- Some linear algebra (essentially taken from the
book by Andersson and Böiers) available
here .
- My hand-written lecture notes,
p 1-7,
p 8-16
p 17-24
p 25-37
p 38-46
p 47-56
p 57-79
p 80-92
p 83-99
p 100-106
- Some old exam papers are available:
1,
2,
3,
4,
5,
6.
NB: These are good exercises, and in my
exam, I will try to follow style and
level. However, my exam my not be exactly the same as those of
the previous lecture, and they may differ from one year to the next!
- A list of theory that might come up in the exam is
available here (for reference,
here is the
previous version, not so different)
In general it may be a good idea to check for a better book prices
litterature at for example
www.pricerunner.se .
Examination
The written examination takes place on June 3. Calculators and
collections of formulas etc. are not allowed during the exam, only
pencil and eraser may be used (paper to write on will be distributed
by the exam organiser.
In addition to the written exam, a compulsory computer exerise
must be carried out, and the report be handed in (by e-mail to
wennberg@math.chalmers.se ; om alls möjligt, skicka
mig en pdf-fil. Endast i absolut sista hand vill jag ha
Word-dokument) no later than June 16.
OBS Please observe that at this date I want the report to be
handed in in final form, and hence it may be a good idea to show me
a preliminary version before that.
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