Lecture plan
Abbreviations used for the Literature:
- LS … C.C. Lin og L.A. Segel: Mathematics Applied to Deterministic Problems in the Natural Sciences, SIAM Classics in Applied Mathematics.
Selected chapters are also included in the Kompendium by H. Krogstad (which can be found on Blackboard):- Chapter 9: pages 98–122 in HK.
- Chapter 10: pages 123–141 in HK.
- AF … A.C. Fowler: Mathematical Models in the Applied Sciences, Cambridge University Press, 1997, Cambridge.
- Chapter 9 is available for download on Blackboard.
- HK … H. Krogstad: Kompendium, TMA4195 Mathematical Modeling. A download link can be found on Blackboard.
- LO … J.D. Logan: Applied Mathematics, 3rd ed., Wiley 2006.
- Chapter 6 is also included in the Kompendium by H. Krogstad, at pages 61–97.
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- This note is also contained in the Kompendium by H. Krogstad, at pages 167–253.
(Unfortunately, due to copyrights the files on Blackboard cannot be made accesible for download here.)
| Date | Topics | Slides | Lecture Notes | Additional Material / Literature |
|---|---|---|---|---|
| Dimensional analysis | ||||
| Week 34 | Brief overview of the lecture Dimensional analysis Buckingham's Pi-Theorem Flow in a pipe | Slides 1 | Notes 1 | LS Chap. 6.1-6.2; HK Chap. 1; |
| Week 35 | Dimensional analysis - repetition Scaling Example: Sinking object | Slides 2 | Notes 2 | HK Chap. 2; LS, Chap. 6.1; AF Chap. 2.1-2.2; |
| Regular and singular perturbations | ||||
| Regular perturbations | ||||
| Week 36 | Regular perturbations Swinging pendulum Kidney modelling | No slides | Notes 3 | LS Chap. 7-8; HK Chap. 3.3; AF Chap. 3; Slides on kidney modeling |
| Week 37 | Kidney modelling - conclusion Singular perturbations for algebraic equations Singular perturbations for ODEs Enzyme kinetics | No slides | Notes 4 | LS Chap. 9; AF Chap. 4.1-4.2; LS Chap. 10; AF Chap. 9.1-9.3; |
| Week 38 | Enzyme kinetics - conclusion | No slides | Notes 5 | LS Chap. 10; AF Chap. 9.1-9.3; |
| ODE models and dynamical systems | ||||
| Equilibrium points Linear stability theory Non-linear stability Bifurcations | Slides 3 | LO Chap. 6; | ||
| Week 39 | Classification of Bifurcations Example: chemical reactor Population dynamics | Notes 6 | LO Chap. 6; HK, pages 142–166 |
|
| Conservation laws and PDE models | ||||
| Week 40 | Basic concepts Universal conservation law Method of characteristics Shocks and rarefaction waves | No slides | Notes 7 | HK2 Chap. 2; |
| Week 41 | Conservation laws for traffic modeling Shock solutions and rarefaction waves Boundary conditions Flux boundary conditions Modelling of changing road situations | No slides | Notes 8 Riemann Problem Simulated | HK2, Chap. 3; |
| Week 42 | Conservation laws in continuum mechanics Euler and Lagrange formulations Reynold's transport theorem Conservation laws in Lagrangian formulation Conservation of momentum Body and surface forces Stress tensor Newtonian fluids Navier–Stokes equations | No slides | Notes 9 | HK2, Chap. 4; LS, Chap. 13-15 |
| Week 43 | Conservation of energy Shallow water waves Flood waves in rivers Convection and diffusion | No slides | Notes 10 | HK 2, Chap. 4; HK2, Chap. 5; |
| Project and summary | ||||
| Week 44 | Introduction of the project Work on the project | |||
| Week 45 | Work on the project | |||
| Week 46 | Work on the project Project presentations | |||
| Week 47 | Summary Questions (and answers?) | |||