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Aktuell information om 2D1266, Matematiska modeller, analys och simulering, del 1

Course News - FALL 2006


Claes Trygger, Dept. Mathematics,, tel. 7907419
Michael Hanke,, (course administrator), room 4529, tel. 7906278
Erik von Schwerin,, room 4520, tel. 7907113
Jelena Popovic,

NADA Course Secretary and Registration

Irene Hanke,, tel. 7909586.

Course material


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.

Supplementary material

For those unfamiliar with the NADA UNIX environment, the following are recommended : This, and other material handed out during the course will be available at the NADA student expedition.
----- 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.
Part II 
  Dynamical Systems Lecture notes Trygger (handed out later)

Part III 
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 ***.

Laboratory Work

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 an account.
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 be prepared. 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.
Sum 		16 
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)
Sum 		13 

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.

Questioning Hours

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 homework assignments.

EXAM 2001-12-15
EXAM 2002-01-12
EXAM 2002-12-20

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 courses.

Course Directory

The course has a course directory on the UNIX system, /info/mmas
The directory contains textfiles, MATLAB M-files, etc., relevant to the course. Some material (like the homework) will also be downloadable from this web-page

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 here.

Student's comments

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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