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TATM38 Course materials
On this page exercises, lecture notes, and other course materials
are published. Please report typos!
Repetition (if you
need)
Linear ODE's of
order 1 and 2 (part of seminar 2)
Some linear algebra
(part of seminar 3)
Linear
difference equations (part of seminar 12)
Fourier, cos-,
and sin-series (part of seminar 19)
Exercises
Time
continuous models (seminars 1-11)
Time
discrete models (seminars 12-18)
PDE models
(seminars 19-27)
Lecture notes (mainly scanned handwritten notes)
Seminar 1
Modeling with (systems of) ODE's. Exponential and logistic
population growth, predator-prey models, epidemic models.
Seminar 2
Linear and separable ODE's. Logistic equation without and with
fishing term.
Seminar 3
Steady states, phase line, stability for single ODE's. Some linear
algebra. Linear systems of ODE's.
Seminar 4
Phase planes for linear systems, classification, stability. Steady
states, linearization, local stability for non-linear systems.
Seminar 5
The chemostat: equations, steady states, linearization, stability.
Seminar 6
From local to global phase-plane picture. Direction fields,
nullclines.
Seminar 7
Phase plane for the chemostat, biological interpretations.
Seminar 8 exercises
Seminar 9
Predator-prey models. Lotka-Volterra equations and modifications,
phase portraits, steady states, stability.
Seminar 10
Populations in competition. Epidemic models, introduction.
Seminar 11
SIS, SIR, SIRS and SEIR epidemic models for spread of infectious
diseases.
Seminar 12
Discrete models. Linear difference equations. Fibonacci's rabbits,
model for propagation of annual plants.
Seminar 13
Linear systems of difference equations. Model for red blood cell
production.
Seminar 14
Non-linear (systems of) difference equations. Steady states,
linearization, stability. Time discrete SIR epidemic model.
Seminar 15
Logistic map, fixed points, stable oscillations, bifurcations,
chaos. Cobwebs.
Seminar 16 exercises
Seminar 17
Population genetics.
Seminar 18
Age structure of populations, Leslie matrices.
Seminar 19
Modeling with PDE's. The conservation and heat/diffusion
equations. Fourier, sin- and cos-series.
Seminar 20
Solving IBVP's with separation of variables and Fourier series.
Seminar 21
IBVP's with non-homogeneous boundary conditions. Diffusion
equation with extra terms. IBVP's in two space dimensions.
Seminar 22
Pattern formation (morphogenesis). Aggregation of cellular slime
molds.
Seminar 23
Chemical basis for morphogenesis. Turing diffusive instability and
pattern formation.
Seminar 24
More on Turing diffusive instability. Aggregation in two space
dimensions.
Seminar 25
Diffusion driven pattern formation in two space dimensions.
Seminar 26 exercises
Seminar 27
Glycolytic oscillator without and with diffusion, 1D and 2D.
Patterns in cellular automata.
Seminars 28-30 presentations of projects
Extras: ML/AI stuff
Neural networks
Principal component
analysis (PCA)
Sidansvarig: goran.bergqvist@liu.se
Senast uppdaterad: 2024-08-30