| TATM38 |
Mathematical Models in Biology, 6 ECTS credits.
/Matematiska modeller i biologi/
For:
BME
KeBi
MED
TB
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Prel. scheduled
hours: 60
Rec. self-study hours: 100
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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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 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
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Courses in Analysis and in Linear Algebra
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.
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Organisation:
This course consists of lectures and problem solving sessions and of a
project work presented in a written report.
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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.
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Course literature:
Edelstein - Keshet, L. Mathematical Models in Biology ISBN-13:
978-0-898715-54-5
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Examination: |
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Written examination
Written reports
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4,5 ECTS
1,5 ECTS
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Course language is Swedish/English.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Stefan Rauch
Link to the course homepage at the department
Course Syllabus in Swedish
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