Plan
This plan is just tentative and it will be subject to changes.
| Week | Days | Theme | Homework | Remarks |
|---|---|---|---|---|
| 34 | Aug 17, 20 | Introduction Dimensionsional analysis | Lin and Segel ch 6, notes by Krogstad, notes by Hanche-Olsen Introduction (slides). Buckingham's Pi proof. |
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| 35 | Aug 24, 27 | Summary of Dimensional Analysis Scaling Example: Falling bullet Regular perturbation | Exercise 1 | |
| 36 | Aug 31, Sep 3 | The projectile problem Flo-Jo's 100m world record Kidney modeling | Self-study: Slides on kidney modeling Self-study: Flo-Jo's 100m world record (see note of the course). |
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| 37 | Sep 7, 10 | Singular perturbation | Exercise 2 (first graded exercise, deadline 9th of September) | Chapert 9 in Lin and Segel. Supervision of the first graded homework (Sep. 7th and 9th) |
| 38 | Sep 14, 17) | Chemical reaction kinetics | Exercise 3 (examples and problems on singular perturbation, supervision on the 17th between 8:15 and 10 in F2) | Slides on elementary chemical reactions and enzyme catalysis. Chapert 10 in Lin and Segel. |
| 39 | Sep 21, 24 | The logistic equation the world population Competition for resources Lotka-Volterra models | Exercise 4 (graded exercise set) | Read Population Models (or chapter on Population Models in the note) Equilibria Kreyszig (9th edition) chp. 4.3-4.5 (3.3-3-5 in 8th ed.) Matlab file showing the various types of linear vector fields in 2D and their equilibria (four main cases). Solution of the logistic equation. Bifurcation theory example Slides on quenching reaction Ch. 10 and 12 in Jordan and Smith. Differential equations, dynamical systems and an introduction to chaos. (Hirsch, Smale, Devaney) ch. 1.2, 1.3, 9.2,11.2 |
| 40 | Sep 28, Oct 1 | Conservation principles 1d conservation laws 1st order PDEs Method of characteristics | Exercise 4 (supervision in class on the 28th of September between 12:15 and 14, regular supervision on the 30th) | Notes: On the method of characteristics Solution of first order PDEs Endimensjonale konserveringslover Section 1 and 2.1-2.4 of the note on "Models based on conservation principles". (Supervision of the second graded homework September 28th and 30th) |
| 41 | Oct 5, 8 | Traffic modelling | Exercise 4 (last supervision. Deadline to hand in 7th of October) | Section 2.5 and 3 of the note on "Models based on conservation principles" (see also chapter 1 in Holden and Risebro, example on traffic flow included). Self-study: Generalization of the Kinetic theory, section 3.2 of the note "Models based on conservation principles". |
| 42 | Oct 12, 15 | Traffic modeling. Conservation laws in mechanics Flood waves in river | Exercise 5 (third and last graded exercise) | Last part of section 3 and section 4 of the note on "Models based on conservation principles". Boundary value problems for conservation laws. Note: Boundary value problems for conservation laws Self study: Traffic from one to two lanes (see last part of note above and also note by Krogstad). |
| 43 | Oct 19, 22 | Conservation laws in mechanics. Diffusion, properties | section 5 of the note on "Models based on conservation principles". Self-study: Solution of Heat equation using the Fourier transform. Kreyszig (9th edition) chp. 12.6 |
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| 44 | Oct 26, 29 | Intermediate asymptotics Nuclear power plant | Exercise 5 (Supervision in class on the 26th between 12:15 and 14, regular supervision on the 28th. Deadline to hand in 28th of October) | (Supervision of the third graded homework October 26th and 28th). |
| 45 | Nov 2, 5 | MODELING PROJECT | Project presentation and project supervision. Homework: Read through modling project before the next lecture!! |
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| 46 | Nov 9, 12 | MODELING PROJECT | Project supervision | |
| 47 | Nov 16, 19 | MODELING PROJECT | Project supervision and project presentations |