Mathematical Models, Analysis And Simulation, Part 1Course News - FALL 2008
TeachersJesper Oppelstrup,jespero@nada.kth.se.removethis, tel. 790 6228
Michael Hanke, hanke@nada.kth.se,
(course leader and examiner), room 4529, tel. 790 6278
Jelena Popovic, jelenap@kth.se.removethis, room 1522, tel 790 7187
Jon Häggblad, jonhagg@csc.kth.se.removethis, room 4520, tel 790 7113
Course materialBookGilbert Strang, Computational Science and Engineering, Wellesley-Cambridge, 2007 or later. Ask your course leader. You may want to check out the prices at some internet bookshop like amazon or bokus.Course Handouts
Supplementary materialFor those unfamiliar with the NADA UNIX environment, the following are recommended :
Preliminary Lecture Schedule
E3, E31, E51: Lindstedtsv. 3
D41: Lindstedtsv. 5
Q31: Osquldas v. 6
brun, gra, spel: computer rooms
Week When Where Who HW Subject
36 Mon 1/9 15-17 E35 All Introduction, overview
Wed 3/9 15-17 E3 O Linear systems of equations, factorizations
Thu 4/9 15-17 E31 O HW1 ?
37 Mon 8/9 15-17 Q31 O Quadratic forms, vector spaces, fundamental subspaces
Wed 10/9 15-17 E3 O Inner product, norm, distance.
Singular value decomposition
Fri 12/9 15-17 rod S HW2 Lab
38 Mon 15/9 15-17 Q31 O Modelling by differential equations.
Linear ODEs
!! Wed 17/9 15-17 E3 O !! RESCHEDULED !!
Wed 17/9 10-12 D41 O Phase plane and state space. The linear case
Thu 18/9 15-17 E31 O Nonlinear equations: Phase plane analysis by linearization
39 Mon 22/9 15-17 Q31 O Energy considerations, Lyapunov functions
!! Wed 24/9 15-17 E3 O !!RESCHEDULED!!
Wed 24/9 10-12 1537 O Limit cycles, bifurcations, center manifold theorem
Fri 26/9 15-17 rod S HW3 Lab
40 Mon 29/9 15-17 Q31 O Modelling by energy considerations.
Primal and dual problems.
Lagrange multipliers, saddle points
!! Wed 1/10 15-17 E3 O !! RESCHEDULED !!
Wed 1/10 10-12 1537 O Modelling of trusses.
Hookes' law, force balance, over/underdetermined structures
41 Mon 6/10 15-17 Q31 O Linear electrical networks, Kirchhoff's and Ohm's laws.
Stationary and frequency analysis
Wed 8/10 15-17 E3 H Practical network analysis: DAEs
Thu 9/10 13-15 rod S Lab
42 Mon 13/10 15-17 Q31 H Introduction to singular perturbations
Tue 14/10 15-17 E31 H Approximation of DAEs, stiff problems
Wed 15/10 15-17 E3 H HW4 FEM for DEs
43 ------ no classes -----
44 Tue 28/10 15-17 E35 H HW5 FEM continued. Iteration methods
Thu 30/10 15-17 E31 H (Fast) Fourier transform and applications.
Interpolation and approximation, aliasing, Shannon/Nyquist
45 Tue 4/11 15-17 E35 H Spectral methods
46 Tue 11/11 15-17 E35 H HW6 Advection, heat, and wave equations
47 Tue 18/11 15-17 E35 H Continuation, method of characteristics
48 Tue 25/11 15-17 D41 H Difference methods, stability and convergence
49 Thu 4/12 15-17 E31 H HW7 Conservation laws
50 Tue 9/12 15-17 E31 H Review, Q & A, old exam paper
------- 2009 --------
02 HW8
*IMPORTANT*
Examination paper will be given on January 8, 2009 in E33, E34 at 9-13.
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. Terminals are booked for this course as shown in the schedule. Moreover, you can work on your own. For that, you can borrow CD-ROMs with Matlab and Comsol Multiphysics at the KTH library. 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.
HW # Due Score Contents
week
---------------------------
1 36 3 Linear Algebra (easy)
2 37 3 Matlab Intro, SVD, Applications
3 39 7 Dynamical systems, phase plane
4 42 6 Circuit Analysis
Here is a short introduction to the modified nodal analysis.
Subsum 20
5 44 6 Singular perturbations, enzyme kinetics
6 46 7 Adaptive FEM in 1D
the m-files you need for hw6 as an ascii-file
7 48 7 DFT and spectral methods
8 02 7 Micro project: Modeling with comsol
Here is a crash course on Comsol Multiphysics.
Subsum 27, Sum Total 47
Questioning HoursThe instructors will be available for questions at the following times during weeks 36-50 with the exception of week 43.TBC: Jelena Popovic: Thursday, 9-10. Jon Häggblad: Monday, 9-10. Credits for HomeworkA list of the accumulated credits is found hereExamsThe 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.To pass the laboratory work requires 20 credits from the homework assignments. More details about the course requirements and grading will be announced soon.
Here are some examples:
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 !
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