Timetable: Monday: 12.15-15.00 (room 7.17); E-lab. 7.01 is booked for
this course on Monday (from 15.00 till 18.00).
Course outline: In semester 8, the course consists of one 2-block lecture
a week and a project in Mathematical Modelling. During the thirteen
weeks of this semester you will be introduced to a selection of
the following topics in mathematical modelling:
- Concepts of mathematical modelling in science and engineering
applications; computational experiments as a tool in engineering
applications.
- Well-posedness of mathematical models and examples of ill-posed
models.
- Discrete and continuous mathematical models.
- Linear and nonlinear systems.
- Stability and linearisation of mathematical models.
- Dissipation and dispersion: physical and numerical.
- Modelling bifurcation and hysteresis effects.
- Mathematical models for continuum mechanics applications.
- Fundamentals of modelling for electromagnetic applications.
- A priori and a posteriori analysis; examples of their applications
for discretised systems.
- Stationary and nonstationary iterative methodologies.
- Projective type algorithms and eigenvalue problems.
- Nonlinear systems and numerical optimisation.
- PDE discretisation methodologies.
- Finite elements and spectral methods.
- Collocation methods and applications.
- Coupled problems in engineering applications.
- Domain decomposition methodologies.
- Inverse problems and their solution techniques.
- Introduction to parallel computing techniques.
Policy statement: Your attendance and promptness are quite important for this
class. You are encouraged to collaborate on different aspects
of your projects with your fellow students. Three other points
to pay attention to are:
- The final report should be signed by all members of the group.
If the report is not signed by a student, it is assumed that s/he
has not contributed to its completion.
- The report will be evaluated under the assumption that each
student in the group has contributed equally to the final outcome.
If it is not the case, a written statement on respective contributions
of each student in the group should be made and attached to the
final report.
- You have to give proper acknowledgment (e.g., in the reference
section in the end of your report) of all works (papers, books,
web pages, etc) which you have used in preparing your report.
Reports without such acknowledgments will not be evaluated.
Important dates: In planning your activities in this course, it is important
to remember two dates:
- Mathematical Modelling Seminar: May 3rd, 2004.
- The deadline for handing-in the final report: May 14th, 2004,
16.00. No later reports will be accepted under any circumstances.
Assessment: The assessment in this course is on the pass/fail basis and
will consist of
- Semester project evaluation (60% of your total assessment),
and
- Written closed-book test (40% of your total assessment): 4 multiple-choice
questions, each worth 10%
In order to pass the course, you will need to achieve at least
40% in your project and minimum 20% in your final test (the later
is equivalent ot answering correctly 2 out of 4 questions). Each
project is to be completed in a group of 4 students (in exceptional
cases, 3 students in a group may be allowed). You will present
your project at a seminar that will be organised in May. Your
presentation will be evaluated, and final decision about your
project assessment will be made by a team of at least 2 professors
on the basis of your written report of around 30 pages. Detailed
guidelines for preparing your project are provided on a separate
MMM information sheet.
Course material and auxiliary references: There are no prescribed textbooks in this course that you
have to buy. However, there are (at least) two books that should
be quite useful in the course. They are:
- Bellomo, N., Preziosi, L., Modelling Mathematical Methods and
Scientific Computation, CRC Press, 1995.
- Quarteroni, A., Sacco, R., and Saleri, F., Numerical Mathematics,
Springer, 2000.
These books should be possible to borrow from the library on a
limited-time loan. However, your own lecture notes will be the
main reference in this course. The University library has a number
of books on the topics pertinent ot the course, and the use of
additional literature in the course is highly encouraged. Some
additional materials may be placed at http://www1.sdu.dk/nat/mci/rm/teaching.html.
Finally, working on your project, you will discover other useful
references that should help you in this course.
At least one of the instructors will be available for consultations
once a week. The specific times allocated for such consultations
will be advised shortly after the semester starts.