Mathematical Models in Biology, 6 credits (TATM38)

Matematiska modeller i biologi, 6 hp

Main field of study

Mathematics Applied Mathematics

Level

Second cycle

Course type

Programme course

Examiner

Stefan Rauch

Director of studies or equivalent

Jesper Thorén

Available for exchange students

Yes
Course offered for Semester Period Timetable module Language Campus VOF
6CKEB Chemical Biology, M Sc in Engineering (Industrial Biotechnology and Production) 7 (Autumn 2017) 1 3 Swedish/English Linköping o/v
6CMED Biomedical Engineering, M Sc in Engineering 7 (Autumn 2017) 1 3 Swedish/English Linköping v
6CMED Biomedical Engineering, M Sc in Engineering (Biomedical Imaging and Visualization) 7 (Autumn 2017) 1 3 Swedish/English Linköping v
6CMED Biomedical Engineering, M Sc in Engineering (Biomedical Materials) 7 (Autumn 2017) 1 3 Swedish/English Linköping v
6CMED Biomedical Engineering, M Sc in Engineering (Biomedical Modelling) 7 (Autumn 2017) 1 3 Swedish/English Linköping v
6CTBI Engineering Biology, M Sc in Engineering (Industrial biotechnology and production) 7 (Autumn 2017) 1 3 Swedish/English Linköping o/v
6CTBI Engineering Biology, M Sc in Engineering (Devices and Materials in Biomedicine) 7 (Autumn 2017) 1 3 Swedish/English Linköping o/v
6CKEB Chemical Biology (Protein Science and Technology) 9 (Autumn 2017) 1 3 Swedish/English Linköping o/v
6MBME Biomedical Engineering, Master's programme 3 (Autumn 2017) 1 3 Swedish/English Linköping v

Main field of study

Mathematics, Applied Mathematics

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Chemical Biology, M Sc in Engineering
  • Biomedical Engineering, M Sc in Engineering
  • Engineering Biology, M Sc in Engineering
  • Chemical Biology
  • Biomedical Engineering, Master's programme

Specific information

This course cannot be included in the same degree as the course TATA51.

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Courses in Analysis and in Linear Algebra

Intended learning outcomes

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 one-dimensional equations
  • find equilibrium points and perform stability analysis for discrete one- and two-dimensional 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

Course content

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.

Teaching and working methods

This course consists of lectures and problem solving sessions and of a
project work presented in a written report.

Examination

UPG1Project reportsU, G1.5 credits
TEN1Written examinationU, 3, 4, 54.5 credits

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Stefan Rauch

Education components

Preliminär schemalagd tid: 60 h
Rekommenderad självstudietid: 100 h

Course literature

Leah Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics 46, ISBN-13: 978-0-898715-54-5
Leah Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics 46, ISBN-13: 978-0-898715-54-5
UPG1 Project reports U, G 1.5 credits
TEN1 Written examination U, 3, 4, 5 4.5 credits

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

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