Lecture Plan

Note that included notes and slides are from 2022 course (and were also used in the 2023 course). The 2024 course will mainly follow the same curriculum. However, the contents of the course may vary somewhat from year to year, and the notes will then be updated.

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 this course's Blackboard page. Due to copyright, the files on Blackboard cannot be made accessible for download here
  • 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.
  • HK2 … Models based on conservation principles
    • This note is also contained in the Kompendium by H. Krogstad, at pages 167–253.
Date Topics Slides Lecture Notes Taped Lectures Additional Material / Literature
Dimensional analysis, scaling
Week 34 Brief course overview
Dimensional analysis
Ship design
Buckingham's Pi-theorem 		Slides 1 Notes 1 Movie 1_1 Movie 1_2 LS Chap. 6.1-6.2; HK Chap. 1;
Week 35 Scaling
Sinking ball
Turbulence 		Slides 2 Notes 2 Movie 2_1 Movie 2_2 Movie 2_3 Movie 2_4 HK Chap. 2; LS, Chap. 6.1; AF Chap. 2.1-2.2;
Regular and singular perturbation
Week 36 Regular perturbations
Projectile problem
Swinging pendulum
Kidney modelling 		Slides on kidney modeling Notes 3 Movie 3_1 Movie 3_2 Movie 3_3 Movie 3_4 LS Chap. 7-8; HK Chap. 3.3; AF Chap. 3;

Week 37 Kidney modelling - conclusion No slides Notes 4 Movie 4_1 Movie 4_2 Movie 4_3 Movie 4_4
LS Chap. 9; AF Chap. 4.1-4.2;

LS Chap. 10; AF Chap. 9.1-9.3;
Week 38 Singular perturbations for algebraic equations and ODEs
Enzyme kinetics 		No slides Notes 5 Movie 5_1 Movie 5_2 Movie 5_3 Movie 5_4 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 Stability
Equilibrium points
Linearization
Amoeba and chemotaxis 		Notes 6 Movie 6_1 Movie 6_2 Movie 6_3 Movie 6_4 LO Chap. 6;

HK, pages 142–166
Conservation laws and PDE models
Week 40 Limit cycles
Bifurcation
Chemical tank
Population models, whale and krill 		No slides Notes 7 Movie 7_1 Movie 7_2 Movie 7_3 Movie 7_4 HK2 Chap. 2;
Week 41 Universal conservation laws, flux densities, sources
Method of characteristics
Riemann problem
Rarefaction waves 		No slides Notes 8

Riemann Problem Simulated 		Movie 8_1 Movie 8_2 Movie 8_3 Movie 8_4 HK2, Chap. 3;
Week 42 Shocks, Rankine-Hugoinot
Boundary conditions
2-phase flow in porous media 		No slides Notes 9 Movie 9_1 Movie 9_2 Movie 9_3 Movie 9_4 HK2, Chap. 4;
LS, Chap. 13-15
Week 43 Traffic modelling
Systems of equations
Reynold's transport theorem 		No slides Notes 10 Movie 10_1 Movie 10_2 
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^ 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 Deliver report by Nov.23
2024-08-13, Dag Wessel-Berg