Upp till *kursens hemsida*.

- Course Fall '06 starts in E3 on Wednesday, Aug. 30, 2006 at 15 o'clock

`trygger@math.kth.se.removethis`

, tel. 7907419
Michael Hanke,

`hanke@nada.kth.se`

,
(course administrator), room 4529, tel. 7906278
Erik von Schwerin,

`schwerin@nada.kth.se.removethis`

, room 4520, tel. 7907113
Jelena Popovic,

`xxxxx@nada.kth.se.removethis`

`ireneh@nada.kth.se.removethis`

, tel. 7909586.
- Course announcement
- Schedule: Lectures and Homework.
- Some lecture notes
- Sample exam papers and solutions

- The NADA UNIX Environment (in English)
- Användarhandledning för UNIX av Berkeleytyp.
- Användarhandledning för MATLAB på NADA
- Användarhandledning för GnuEmacs och Mg
- Användarhandledning för Terminalsalarna och "X"
- Översikt över datormiljön på NADA.
- Regler för datoranvändning på Nada.

----- 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 --------

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 *IMPORTANT* Examination paper given *** Not yet scheduled ***.

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.

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 week --------------------------- 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.

Erik von Schwerin : TBA

jelena Popovic : TBA

EXAM 2001-12-15

EXAM 2002-01-12

EXAM 2002-12-20

`/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

Upp till *kursens hemsida*.

Sidansvarig: <hanke@nada.kth.se>

Senast ändrad 08 juni 2006

Tekniskt stöd: <webmaster@nada.kth.se>