Mathematical Models, Analysis And Simulation, Part 1Results of re-examAs of Thu, June 9, the graded re-exams are available at the "student expedition".Re-examTHE RE-EXAM WILL TAKE PLACE TUE JUNE 7, 8-13.Room 1537, floor 5, Lindstedtsvägen 3. Please register for the exam by sending an email to Jon. ( jonhagg@csc.kth.se.removethis).
The exam that was given on Jan 13, 2011, can be downloaded here. Course News - FALL 20102011-04-01:THE RE-EXAM WILL TAKE PLACE TUE JUNE 7, 8-13. Room 1537, floor 5, Lindstedtsvägen 3.2011-01-18:We are currently grading the exam. In the mean time, please fill out the course evaluation! 2011-01-12:Welcome to the exam tomorrow! As posted further below, the exam is scheduled for 2011-01-13, 14-19 in D41-42. It is a closed book examination. I.e. no books, notes or calculators are allowed. GOOD LUCK TO ALL OF YOU! A few of you who will not take the exam tomorrow have asked about the re-exam. Currently, the first re-exam is scheduled to take place in June. 2010-12-08: A summary of the course have been posted below together with the lecture notes. It gives references to Strang and lists definitions that should be known and questions that you should be able to answer. It is intended to be a help in your preparation for the exam. Read the book (the indicated chapters), the lecture notes, the assignments that you have done, and also check out the old exams posted below. We did not cover conservation laws, so questions on conservation laws will not appear on your exam. We did however do more on Fourier series and spectral methods than before. 2010-12-07: EXTENDED deadline for HW6, see below. 2010-12-07:During the lecture yesterday, copies of some pages regarding spectral methods were handed out. If you did not get a copy, come and get one in my office. During the lecture we worked through (in detail) the derivation of a pseudo spectral method for the incompressible Navier-Stokes equations. It was all done on the board, but the copy hnaded out contains a lot of information. 2010-11-24:Lecture on Wed Dec 1 will cover the rest of the handout that has now been posted, on "Spectral interpolation, differentiation and spectral methods for PDEs". Today we covered interpolation and differentiation, next Wed we will talk about Galerkin and collocation spectral methods for PDEs. 2010-11-24:A complete HW6 has been posted.(Possibly with mistakes and misprints - let me know). 2010-11-21:First part of HW6 posted, second part will follow soon. Deadline of HW extended until Thu Dec 9. 2010-11-21: To prepare for lecture on Wed Nov 24, read section 4.1 in Strang (if you ahve not already done so, this we covered last week), section 4.3 (started on this last lecture) and also section 4.5. 2010-10-29:Plan for the block of lectures on PDEs:
2010-10-26:Regarding HW4:
2010-10-19:EXTENDED DEADLINE FOR HW4. See below. 2010-09-14:The book is now available at Kårbokhandeln. 2010-09-09: The book will be available at Kårbokhandeln in the beginning of next wek, week 37. The course has now started. Lecture notes and homeworks will be available as we go along... See below. TeachersAnna-Karin Tornberg,annak@nada.kth.se.removethis,
(course leader and examiner), room 4517, tel. 790 6266
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
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, E35, E53: Lindstedtsv. 3
D41: Lindstedtsv. 5
L22: Drottning Kristinas väg 30KV
Week Lecture When Where
number
v35 L1 Tue 31/8 15-17 E31
v35 L2 Thu 2/9 15-17 E35
v36 L3 Wed 8/9 15-17 E32
v37 L4 Wed 15/9 10-12 L22
v38 L5 Thu 23/9 15-17 E35
v39 L6 Tue 28/9 15-17 E52
v39 L7 Thu 30/9 15-17 E52
v40 L8 Tue 5/10 15-17 E31
v40 L9 Thu 7/10 15-17 E52
v41 L10 Tue 12/10 15-17 E31
v43 L11 Mon 25/10 15-17 E35
v43 L12 Wed 27/10 15-17 E35
v44 L13 Wed 3/11 15-17 E35
v45 L14 Wed 10/11 15-17 E31
v46 L15 Wed 17/11 15-17 E35
v47 L16 Wed 24/11 15-17 E35
v48 L17 Wed 1/12 15-17 D41
v49 L18 Mon 6/12 15-17 E35
v49 L19 Wed 8/12 15-17 D41
Tentative outline of lecturesLinear 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.Ordinary Differential Equations (ODEs), 7 lecturesModeling by differential equations. Non-dimensionalization and scaling. Linear ODEs. Phase plane and state space. Nonlinear equations, phase plane analysis by linearization. Energy considerations. Lagrange multipliers. Primal and dual problems.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, 3 lecturesFast fourier transform (FFT) - properties and applications. Interpolation and approximation. Aliasing. Spectral methods for the numerical solution of PDEs.Summary, remarks and connections, 2 lecturesWrapping 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 prefer, you can work on your own computer. For that, you can borrow CD-ROMs with Matlab 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 maxmimum amount of credit for a report. You may infer from this our estimate of the amount of work necessary.
TENTATIVE SCHEDULE FOR HOMEWORK
HW # Due Maximum Contents
date Score
---------------------------
1 6/9 3 Linear Algebra
2 20/9 3 Matlab Intro, SVD, Applications
3 4/10 7 Dynamical systems, phase plane
4 28/10 6 Circuit Analysis (OBS! New date, updated Oct 19).
5 15/11 6 PDE
6 7/1 6 DFT and spectral methods (OBS! New date, updated Dec 7).
OBS! Handing in homeworks after due date will cause a 50% reduction in credit given.Downloads and comments:
Questioning HoursThe lab instructor will be available for questions at the following times during weeks 35-50:Jon Häggblad: Wed 8.30-9.30, Fri 15-16. 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 place2011-01-13, 14-19 in D41-42.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.
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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