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Mathematical Models in Biology, 6 credits
Matematiska modeller i biologi, 6 hp
TATM38
Main field of study
Mathematics Applied MathematicsCourse level
Second cycleCourse type
Programme courseExaminer
Stefan RauchDirector of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 60 hRecommended self-study hours: 100 h
Available for exchange students
YesECV = 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, Valla | E |
| 6CMED | Biomedical Engineering, M Sc in Engineering (Biomedical Imaging and Visualization) | 7 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | E |
| 6CMED | Biomedical Engineering, M Sc in Engineering (Biomedical Materials) | 7 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | E |
| 6CMED | Biomedical Engineering, M Sc in Engineering (Biomedical Modelling) | 7 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | E |
| 6MBME | Biomedical Engineering, Master's programme | 3 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | E |
| 6CKEB | Chemical Biology (Protein Science and Technology) | 9 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | C/E |
| 6CKEB | Chemical Biology, M Sc in Engineering (Industrial Biotechnology and Production) | 7 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | C/E |
| 6CTBI | Engineering Biology, M Sc in Engineering (Devices and Materials in Biomedicine) | 7 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | C/E |
| 6CTBI | Engineering Biology, M Sc in Engineering (Industrial biotechnology and production) | 7 (Autumn 2017) | 1 | 3 | Swedish/English | Linköping, Valla | C/E |
Main field of study
Mathematics, Applied MathematicsCourse level
Second cycleAdvancement level
A1XCourse 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 AlgebraIntended 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
| UPG1 | Project reports | 1.5 credits | U, G |
| TEN1 | Written examination | 4.5 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Stefan RauchCourse website and other links
http://www.mai.liu.se/und/kurser/index-amne-tm.htmlEducation components
Preliminary scheduled hours: 60 hRecommended 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.
Course literature is preliminary.
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
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TEN1
|
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| 1.2 Fundamental engineering knowledge (G1X level) |
X
|
X
|
X
|
TEN1
|
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
|
|
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
|
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
|
X
|
X
|
TEN1
|
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| 2.2 Experimentation, investigation, and knowledge discovery |
|
|
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| 2.3 System thinking |
|
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| 2.4 Attitudes, thought, and learning |
|
X
|
X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
|
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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|
X
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| 3.3 Communication in foreign languages |
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|
X
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 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 |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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