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.
- This note is also contained in the Kompendium by H. Krogstad, at pages 167–253.
|Date||Topics||Slides||Additional Material / Literature|
|Week 34|| Brief overview of the lecture |
Flow in a pipe
|Wednesday||LS Chap. 6.1-6.2; HK Chap. 1;|
|Week 35|| Dimensional analysis - repetition |
Example: Sinking object
|HK Chap. 2; LS, Chap. 6.1; AF Chap. 2.1-2.2;|
|Regular and singular perturbations|
|Week 36|| Regular perturbations |
|Wednesday|| 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
LS Chap. 9; AF Chap. 4.1-4.2;
LS Chap. 10; AF Chap. 9.1-9.3;
|Week 38||Enzyme kinetics - conclusion||Wednesday||LS Chap. 10; AF Chap. 9.1-9.3;|
|ODE models and dynamical systems|
| Equilibrium points |
Linear stability theory
|LO Chap. 6;|
|Week 39|| Classification of Bifurcations |
Example: chemical reactor
| Wednesday |
| 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
|HK2 Chap. 2;|
|Week 41|| Conservation laws for traffic modeling |
Shock solutions and rarefaction waves
Flux boundary conditions
Modelling of changing road situations
|Wednesday||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
|Wednesday|| HK2, Chap. 4;
LS, Chap. 13-15
|Week 43|| Conservation of energy |
Shallow water waves
Flood waves in rivers
Convection and diffusion
| 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 |
|Week 47|| Summary |
Questions (and answers?)