Mathematical Models, Analysis And Simulation, Part 1 (matmod11)
Course News - FALL 2011
2012-01-23: The re-exam will be given on February 18, 9.00-13.00. It will be in B22 and B23, at Brinellvägen 23, opposite to KTH-hallen. The final exam that was given in December can be found here , together with some solution sketches.
Please send me (Anna-Karin) an email if you plan to take the re-exam!
2011-12-07: To confirm what I said in class: the due date for the homework on spectral methods has been postponed by two days, and is due today Wednesday Dec 7. (Meaning we pick them up Thu morning).
2011-11-23: The exams from last year have been posted below.
2011-11-23: A handout on spectral methods for PDEs was handed out during the lecture on Monday. It is not posted online due to copyright.
2011-11-09: In class today, I did not manage to cover everything on hyperbolic PDEs that I had planned. Therefore, the due date for the homework on PDEs has been postponed by three days, to Thursday Nov 17.
2011-11-09: The questioning hour by Jennifer Gruenig next Wed (Nov 16) is cancelled.
2011-10-26: A handout with a simple introduction to PDEs was handed out during the lecture today. It is not posted online due to copyright.
2011-09-20: The fact that you can work with your homeworks all day the day when homework is due, and drop it off as late as you want is clarified below. The second homework has been posted.
2011-09-01: The first homework was posted before the first lecture. Now you can also find lecture notes on Linear Algebra, part 1 and 2 to download. (These are the ones already handed put in class).
2011-08-29: If you are not sure if you are registered for the class or not, come to the first lecture anyway. Sort out the issue with regsitration with the administrative staff at the student office, "Student expeditionen" at floor 2 of Qsquars Backe 2.
2011-07-06: The first lecture will take place Tue August 30 2011, 10-12, in D34 (Lindstedtsvägen 5).
2011-07-06: 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. Note however, that the book is different. See below.
All our rooms are in the same corridor on floor 5 that can be reached from the D or E building, i.e. from the entrances at Lindstedtsvägen 3 and 5 and at Osquars Backe 2.
Questioning HoursThe lab instructors will be available for questions at the following times during weeks 35-50:
Jon Häggblad: Fri 14-16.
Jennifer Gruenig: Wed 9-11.
You are strongly encouraged to make use of this opportunity to ask queastions and discuss homework topics!
BookGilbert 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 notesLecture notes will be posted here, as they become available.
Supplementary materialFor those unfamiliar with the NADA UNIX environment, the following are recommended :
Preliminary Lecture Schedule
E31: Lindstedtsv. 3 D34, D41: Lindstedtsv. 5 L51, L52: Drottning Kristinas väg 30 Q21,Q31: Osquldas väg 6B V23: Teknikringen 72 V34: Teknikringen 76 Week Lecture When Where number v35 L1 Tue 30/8 10-12 D34 v35 L2 Thu 1/9 10-12 V34 v36 L3 Mon 5/9 13-15 E31 v36 L4 Thu 8/9 13-15 E31 v38 L5 Mon 19/9 13-15 Q31 v38 L6 Thu 22/9 13-15 L51 v39 L7 Thu 29/9 10-12 L52 v40 L8 Thu 6/10 10-12 Q21 v41 L9 Wed 12/10 10-12 D34 v43 L10 Wed 26/10 10-12 D34 v43 L11 Fri 28/10 10-12 L51 v45 L12 Mon 7/11 10-12 V23 v45 L13 Wed 9/11 10-12 D41 v46 L14 Mon 14/11 10-12 D34 v46 L15 Fri 18/11 10-12 E31 v47 L16 Mon 21/11 10-12 E31 v47 L17 Wed 23/11 10-12 D34 v49 L18 Mon 5/12 10-12 D34
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 lecturesStructures in equilibrium. Energy considerations. Minimum principles. Incidence matrices. Lagrange multipliers.
Ordinary Differential Equations (ODEs), 3 lecturesModeling 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 lecturesModeling (continuous in space). Advection, heat and wave equations. Conservation laws. Well-posedness. Separation of variables. Numerical discretization. Consistency, stability and convergence.
PDEs continued: The Fast Fourier Transform and Spectral methods, 4 lecturesFast fourier transform (FFT) - properties and applications. Interpolation and approximation. Aliasing. Spectral methods for the numerical solution of PDEs.
Summary, remarks and connections, 1 lectureWrapping up the course, making connecting remarks between different modules. Example problems for exam.
Laboratory WorkThe 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 in the NADA mailbox outside the Students' expedition (NOT the instructors' mail stops !), according to the schedule below. Attach a cover page properly filled in. It can be downloaded here or fetched at the Student Expedition. 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 in the Student Expedition.
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 19/9 6 Linear Algebra, Matlab Intro, SVD, Applications 2 3/10 6 Equilibrium problems 3 24/10 6 Dynamical systems, phase plane 4 17/11* 6 PDE (* Due date changed, delayed from Mon to Thu) 5 7/12* 6 DFT and spectral methods (* Due date changed, delayed from Mon to Wed)
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:
ExamsThe 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 been scheduled to take place
2011-12-20, 8-13 in K51 & K53.
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.
The NADA Terminal RoomsThe 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 computerIf you have a computer and an internet connection you can access the NADA network from home. Information is found here.
Student's commentsThe 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.