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 ...)

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.
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

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.


Bernt Wennberg <wennberg@math.chalmers.se>