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School of
Electrical Engineering
and Computer Science

Mathematical Models, Analysis And Simulation, Part 1 (matmod12)

Course News - FALL 2012


2012-12-06: I would ask you all to fill out the course evaluation form. Please take the time to make constructive suggestions on improvements!
Click to get course evaluation form:

2012-12-03: Due to the power outage at KTH today, we postpone the deadline for HW5 by one day.
2012-11-30: Under the lecture notes headline, I have posted a pdf with a summary of the course. It goes through the course and specifies what you are expected to know. It is meant as a help for you when you study for the exam.
2012-11-26: Since it seemed ok, the last lecture will be moved to Friday Dec 7, 13-15. It will be held in room 305 at Tekninkringen 14.
2012-11-20: OBS! All students need to sign up to be able to write the exam. You do this through "Mina Sidor". Do it NOW!
2012-11-19: HW5 has been posted below.
2012-11-08: I need to move our last lecture. My suggestion is to move it to Friday Dec 7, 13-15. Please let me know as soon as possible if you have a problem attending at this suggested time.
2012-11-08: The deadline for HW4 has been postponed for a week. The new date is Nov 19.
2012-11-08: The third and last set of lecture notes for the PDE block has been posted below. It covers hyperbolic PDEs.
2012-10-24: HW4 and 2 sets of lecture notes on PDEs are posted below.
2012-10-22: As agreed during the last lecture, HW3 is due Wed Oct 24 instead of today. And,in practice that means that we will pick them up at 10 the day after. So if you have problems getting in to drop off your homework in the evening, you can always do it in the morning.
2012-10-03: Homework 3 has been posted.
2012-09-26: Two more sets of lecture notes have been posted.
2012-09-20: Homework 2 as well as a new set of lecture notes have been posted.
2012-09-17: This week's office hours on Wednesday will be between 15-17. Next week, they will run at the regular time again.
2012-09-13: Remember the deadline for submitting the first homework on Monday Sep 17!! Homeworks can be handed in at the student expedition at the Math department. Once they are closed, your can use the black mail box opposite to the student expedition. Make sure that you have entered your name, the course number, and the instructors name on the front page.
2012-09-13: The last set of lecture notes from the linear algebra part, as well as the first set of lecture notes on equilibrium problems are posted below.
2012-08-29: The schedules for homeworks and for lectures have been posted for a while. The last detail of time for office hours has been updated today. I think we are all ready to start!
2012-06-26: The first lecture will take place Wed August 29 2012, 15-17, in Q33 (Osquldas väg 6B).
2012-06-26: Very little information is posted below as of yet. Look at last years homepage , to get an idea. Some details will change, but much will remain the same.

Teachers

Anna-Karin Tornberg, akto@kth.se.removethis, (course leader and examiner), room 309, tel. 790 6266
Jennifer Gruenig, jgrunig@csc.kth.se.removethis, room 315, tel 790 7187

The address is Teknikringen 14. These are the rooms that we are moving to, and will use from Monday September 17.

Questioning Hours

The lab instructor Jennifer Grenig will be available for questions in her office on Wednesdays 14-16 during weeks 36-50. You are strongly encouraged to make use of this opportunity to ask questions and discuss homework topics!

Course material

Book

Gilbert Strang, Introduction to applied mathematics, Wellesley-Cambridge, 1986. (Going back to the old classic, using supplemental material for some topics). You may want to check out the prices at some internet bookshop like amazon or bokus.

Lecture notes

Lecture notes will be posted here, as they become available.

Preliminary Lecture Schedule

						      
E31, E34, E35:            Lindstedtsv. 3 
E52:            Lindstedtsv. 27 
D34, D41:       Lindstedtsv. 5
L51:       Drottning Kristinas väg 30
Q17,Q33,Q36:        Osquldas väg 6B
V22:            Teknikringen 72
V35:            Teknikringen 76

Week Lecture   When                 Where   
     number
v35    L1      Wed  29/8  15-17      Q33
v35    L2      Fri  31/8  13-15      Q17
v36    L3      Mon   3/9  13-15      L51
v37    L4      Thu  13/9  13-15      Q33
v38    L5      Tis  18/9  13-15      Q36
v38    L6      Thu  20/9  13-15      E31
v39    L7      Mon  24/9  15-17      E31
v40    L8      Tue   2/10 13-15      D34
v41    L9      Tue   9/10 10-12      E31
v43    L10     Mon  22/10 15-17      E34
v43    L11     Tor  25/10 10-12      V22
v45    L12     Mon   5/11 15-17      E35
v45    L13     Thu   8/11 10-12      E31
v46    L14     Wed  14/11 10-12      V35
v47    L15     Tue  20/11 15-17      D41
v47    L16     Thu  22/11 15-17      E52
v48    L17     Tue  27/11 13-15      E31
**** v49    L18     Tue   4/12 13-15      D41 ***** MOVED
Replaced by: 
v49    L18     Fri  7/12  13-15,     305, Teknikringen 14.

Tentative outline of lectures

Linear Algebra, 3 lectures.

Linear system of equations. Least squares and normal equations. Gaussian elimination and LU decomposition. Eigenvalues and eigenvectors. QR factorization. Singular value decomposition. Iterative methods.

Equilibrium problems, 3 lectures

Structures in equilibrium. Energy considerations. Minimum principles. Incidence matrices. Lagrange multipliers.

Ordinary Differential Equations (ODEs), 3 lectures

Modeling by differential equations. Non-dimensionalization and scaling. Linear ODEs. Phase plane and state space. Nonlinear equations, phase plane analysis by linearization.

Partial Differential Equations (PDEs), 4 lectures

Modeling (continuous in space). Advection, heat and wave equations. Well-posedness. Separation of variables. Numerical discretization. Consistency, stability and convergence.

PDEs continued: The Fast Fourier Transform and Spectral methods, 4 lectures

Fast fourier transform (FFT) - properties and applications. Interpolation and approximation. Aliasing. Spectral methods for the numerical solution of PDEs.

Summary, remarks and connections, 1 lecture

Wrapping up the course, making connecting remarks between different modules. Example problems for exam.

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. Homeworks can be handed in at the student expedition at the Math department. Once they are closed, your can use the black mail box opposite to the student expedition. Make sure that you have entered your name, the course number, and the instructors name on the front page. 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. Homework is handed back during class when they are graded.

The NADA computers are available for computer work. If you need an account, go to Delfi, Osquars Backe 2. If you prefer, you can work on your own computer. For that, you can borrow CD-ROMs with Matlab at the KTH library.

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. The "score" indicates the maxmimum amount of credit for a report. 

TENTATIVE SCHEDULE FOR HOMEWORK

HW #  Due    Maximum    Contents
      date    Score
---------------------------
1	17/9 	6	Linear Algebra, Matlab Intro, SVD, Applications
2	1/10 	6 	Equilibrium problems  
3       24/10 	6 	Dynamical systems, phase plane !!OBS, postponed by 2 days. 
4	19/11 	6 	PDE !!OBS, postponed by a week. 
5        4/12   6       DFT and spectral methods !!OBS, posponed by a day due to power outage.

OBS! Handing in homeworks after due date will cause a 50% reduction in credit given.

When a homework is due a certain date, in practice it means that we will pick them up early the day after. Hand in the report (one for each group of max 2 people) in the NADA mailbox outside the Students' expedition. It is outside of the locked doors, so you can access it also late in the evening.

Downloads and comments:

Exams

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 exam has tentatively been scheduled to take place

Tuesday December 11, 8-13 in D34 and D35.

To pass the exam, 18 out of 40 credits is required on the written exam.

To pass the laboratory work requires 15 credits from the homework assignments.

To pass the course, one has to pass both the written exam and the laboratory work. If this minimum requirement is met, then the grade will be based on the sum of credits on the exam (max 40) and credits from the homeworks (max of 30), i.e. a total max of 70.

Old exams

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.

Work on your own computer

If you have a computer and an internet connection 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 !

^ Up to the course's homepage.

Copyright © Published by: Anna-Karin Tornberg <akto@kth.se>
Updated 2012-12-07