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Aktuell information om 2D1266, Matematiska modeller, analys och simulering, del 1
Course News - FALL 2006
- Course Fall '06 starts in E3 on Wednesday, Aug. 30, 2006 at 15 o'clock
Claes Trygger, Dept. Mathematics,
firstname.lastname@example.org, tel. 7907419
(course administrator), room 4529, tel. 7906278
Erik von Schwerin,
email@example.com, room 4520, tel. 7907113
NADA Course Secretary and Registration
firstname.lastname@example.org, tel. 7909586.
Gilbert Strang, Introduction to Applied Mathematics,
Wellesley-Cambridge, 1986 or later. Available at the THS
student union bookshop. You may want to check out the prices
at some internet bookshop like amazon or bokus.
Course Handout - The Binder
The material for the first part of the course is handed out at lecture
1. A binder with most of the material for the rest of the course will
be sold at the student expedition in week 35. More material, in
particular lecture notes,
updates, etc., will be handed out at lectures and will be available at
the student expedition afterwards. Homework texts for the homeworks are
also on the course home page.
- Course announcement
- Schedule: Lectures and Homework.
- Some lecture notes
- Sample exam papers and solutions
For those unfamiliar with the NADA UNIX environment, the following are
This, and other material handed out during the course will be available at the
NADA student expedition.
- The NADA UNIX Environment (in English)
- Användarhandledning för UNIX av Berkeleytyp.
- Användarhandledning för MATLAB på NADA
- Användarhandledning för GnuEmacs och Mg
- Användarhandledning för Terminalsalarna och "X"
- Översikt över datormiljön på NADA.
- Regler för datoranvändning på Nada.
----- Prel. list of material to be handed out -----
The binder, at course start, including
homework texts (also available from home page),
Part I Trygger material, old exam papers, etc.
Dynamical Systems Lecture notes Trygger (handed out later)
Lecture Notes, copies of other material (handed out later)
-------- The End --------
Preliminary Lecture Schedule
E2, E3, E31: Lindstedtsv. 3
L31, L51: drottning Kristinas v 30
var: Computer room karmosin, vit (exception: 13/9, spelhallen)
Week When Where Who HW Subject
35 Wed 30/8 15-17 E3 All Introduction. Linear systems of equations. Factorizations
Thu 31/8 15-17 E3 T Quadratic forms. Vector spaces. Fundamental subspaces
36 Wed 6/9 15-17 E3 T Inner product, norm, distance. Singular value decomposition
Thu 7/9 15-17 E3 T HW1 Electrical networks. Kirhhoff's laws. Ohm's law
37 Mon 11/9 15-17 E3 T Modelling by energy considerations. Primal and dual problems
Wed 13/9 15-17 var S Lab
Thu 14/9 15-17 E3 T HW2 Lagrange multipliers. Lagrangians. Saddle points
38 Won 18/9 15-17 E3 T Modelling of trusses. Hookes' law. Force balance. Over/under-determined structures
Wed 20/9 15-17 E3 T Basics of probability theory. Least-squares estimator
39 Mon 25/9 15-17 E3 T Gauss-Markov estimator. Sequential estimation. Kalman filter (intro)
Tue 26/9 13-15 var S Lab
Wed 27/9 15-17 E3 T HW3 Modelling of an elastic bar. Dual spaces and adjopint operators
40 Mon 2/10 15-17 E3 T Energy considerations. Classical calculus of variations
Tue 3/11 13-15 var S Lab
Wed 4/10 15-17 E3 T Modelling of a plane flow. Green's theorem, divergence, rotation, Gauss theorem
41 No classes
42 No classes HW4 - On Monday, w. 43
43 Wed 25/10 15-17 E2 T Examples of modelling by differential equations. Linear ODEs
Thu 26/10 15-17 E3 T Phase plan and state space. The linear case
Fre 27/10 15-17 E3 T Nonlinear equations: Phase plan analysis by linearization. Hartman-Grobman theorem
44 Mon 30/10 15-17 var S Lab
Wed 1/11 15-17 E2 T HW5 Energy considerations: Lyapunov functions. Limit cycles. Bifurcations
45 Mon 6/11 15-17 E51 H Introduction to singular perturbations (R.E. O'Malley)
Wed 8/11 15-17 E2 H FEM for DE: Strang 5.4, 3.2-3
Fre 10/11 15-17 E2 H FEM continued. Iterative methods: 5.1, 5.3
46 Mon 13/11 10-12 var S Lab
Wed 15/11 15-17 E2 H HW6 (Fast) Fourier Transform, applications: 4.1-3, 5.5
47 Mon 20/11 13-15 E51 H The heat & wave equation: 6.4, 6.5
Wed 22/11 15-17 E2 H Continuation, method of characteristics: 6.5
Fri 24/11 15-17 E3 H Difference methods: 6.5, 6.6
48 Mon 27/11 15-17 var S Lab
Wed 29/11 15-17 E2 H HW7 Stability of finite difference schemes: 6.6
Examination paper given *** Not yet scheduled ***.
The laboratory work consists of homework and computer experiments
carried out by groups of no more than two students. Each group hands
in a report on each assignment to an instructor, or in the NADA
mailbox outside the Students' expedition (NOT the instructors' mail
stops !), according to the schedule below. We strongly prefer paper
hand-ins, the Swedish post office can be relied upon for those unable
to attend in person. Instructors will be available every week at the
questioning hours given below
for help with homework etc. The deadline for
homework week x is Sunday evening.
The NADA computers are available for computer work.
Terminals are booked for this course as shown in the schedule.
You will need a NADA account. Sign the name list sent round and after
a few days go to the help desk (Osquars B. 2, ground floor, open
weekdays 10-12 and 13-15 (except for Friday))
Delfi to obtain
Discussions of homework and assignments with your fellow
students are encouraged. We hope that those of you who are more
experienced in some theoretical aspect, or in the use of computers,
will give advice to others. The assignment reports should be clearly
written and easy to read for the grader. If you use a computer, you
must edit the output and write a descriptive summary.
Mere sheaves of computer plots and printed output
will not be accepted.
Here are some guidelines how a report should
A good example of a nice report can be found here.
The table below shows the homework and computer assignments. There
will be a link to a table of status and results of homework handed
in. The "score" indicates the amount of credit for a passed report.
You may infer from this our estimate of the amount of work necessary.
Incomplete reports may - at the discretion of the grader - be
completed for more credits, usually with a deadline of a few days.
Due week x means due Sunday evening week x (except hw 4, Monday w. 43).
HW # Due Score Contents
1 36 3 Strang Ch 1
2 37 3 Strang Ch 1
3 39 4 Strang Ch 2 + Population Demo
4 43 6 Strang Ch 2-3 + Circuit Analysis
Here is a short introduction to the modified nodal analysis.
5 44 7 Phase Portraits; How to Make Your Own in MATLAB.
6 46 6 Singular perturbations, enzyme kinetics
NOTE: For hw6 you also need the description of the model (in the Binder)
7 48 7 FEM
the m-files you need for hw7 as an ascii-file
8 02 7 Options and the Heat Equation
Here is a crash course on femlab. The shell
script for calling femlab can be obtained here.
Sum 14, Sum Total 43
A copy of the homework formulations can be found in the directory /info/mmas/part1/homeworks.
The instructors will be available for questions at the following times
during weeks 35-40 and 43-50.
Erik von Schwerin : TBA
jelena Popovic : TBA
Credits for Homework
A list of the accumulated credits is found Fall 06 here
The examination paper will be written with closed books. It
will be based on the list of questions and typical problems handed out
during the course. The max. score will be approx. 60, and to pass the course
you must obtain a total score, homework included, of approx. 60.
To pass the laboratory work requires 20 credits from the
The NADA Terminal Rooms
The student union magnetic card gives access to the NADA terminal
rooms around the clock, but daytime they are often booked for other
Course Directory The course has a course directory on
the UNIX system,
contains textfiles, MATLAB M-files, etc., relevant to the course. Some
material (like the homework) will also be downloadable from this
Dial-up or work on your own computer
If you have a computer and a modem you can access the NADA network
from home. Information is found
The course will be evaluated at the end when you will be asked to fill
in a standard course evaluation form, but any comments along the way
are most welcome !
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Senast ändrad 08 juni 2006
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