Mathematical Models in Biology, 6 credits

Matematiska modeller i biologi, 6 hp

TATM38

Main field of study

Mathematics Applied Mathematics

Course level

Second cycle

Course type

Programme course

Examiner

Stefan Rauch

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 100 h

Available for exchange students

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

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 reports1.5 creditsU, G
TEN1Written examination4.5 creditsU, 3, 4, 5

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Stefan Rauch

Course website and other links

http://www.mai.liu.se/und/kurser/index-amne-tm.html

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 100 h

Course literature

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

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. 

Leah Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics 46, ISBN-13: 978-0-898715-54-5

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
X
TEN1

                            
1.2 Fundamental engineering knowledge (G1X level)
X
X
X
TEN1

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
X
TEN1

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork

                            
3.2 Communications
X

                            
3.3 Communication in foreign languages
X

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

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