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Valid for year : 2007
 
TATM38 Mathematical Models in Biology, 6 ECTS credits.
/Matematiska modeller i biologi/

For:   BKM   C   COM   KeBi   TB  

 

Prel. scheduled hours: 60
Rec. self-study hours: 100

  Area of Education: Science

Subject area: Mathematics
  Advancement level (G1, G2, A): A

Aim:
During this course participants will learn to formulate, analyse and interpret mathematical models that are used in biology and biotechnical applications. The participants will learn both mathematics needed for building a model as well as modelling through formulating and solving basic models used in population dynamics, epidemiology and morphogenesis. After this course a student will be able to
  • draw a phase portrait, find equilibrium points and perform stability analysis for one- and two-dimensional dynamical systems
  • calculate and draw explicit solutions of two-dimensional linear systems and simple onedimensional equations
  • find equilibrium points and perform stability analysis for discrete one- and twodimensional dynamical systems
  • formulate and recognise PDE-models based on the continuity equation
  • solve initial-boundary value problem for diffusion equations with the use of the method of separation of variables and the use of Fourier series
  • recognise and solve several classical models in mathematical biology such as
    • logistic growth of population
    • model of chemostat
    • Lotka-Volterra type models för predator-prey and competing species
    • Keller-Segel-model for aggregation of slime molds
    • Turing model of diffusion driven instability in chemical reaction systems
  • read and analyse other mathematical models in scientific literature


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Mathematics corresponding to TATM72 Analysis A, TATM73 Analysis B and TATM31 Algebra M.

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Organisation:
This course consists of lectures and problem solving sessions and of a project work presented in a written report.
Course contents:
Ordinary differential equations. Dynamical systems: phase portrait and linear stability of equilibrium points. Integrals of motion. Chemostat, Lotka-Volterra models for interacting populations and models of epidemics. Linear and nonlinear difference equations modelling populations. Continuity equation. Solving diffusion type equations through separation of variables and the use of Fourier series. Conditions for diffusive instability and a chemical basis for morphogenesis.

Course literature:
Edelstein - Keshet, L. Mathematical Models in Biology ISBN-13: 978-0-898715-54-5
Examination:
Written examination
Written reports
 3 p
1 p
/
/
4,5 ECTS
1,5 ECTS
 


Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Göran Forsling
Examiner: Stefan Rauch
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 05/30/2007