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.
    • This note is also contained in the Kompendium by H. Krogstad, at pages 167–253.
Date Topics Slides Additional Material / Literature
Dimensional analysis
Week 34 Brief overview of the lecture
Dimensional analysis
Buckingham's Pi-Theorem
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
Regular perturbations
Week 36 Regular perturbations
Swinging pendulum
Kidney modelling
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
Enzyme kinetics


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
Non-linear stability
LO Chap. 6;
Week 39 Classification of Bifurcations
Example: chemical reactor
Population dynamics

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
Boundary conditions
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
Stress tensor
Newtonian fluids
Navier–Stokes equations
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
Project presentations
Week 47 Summary
Questions (and answers?)
2018-11-20, Markus Grasmair