| TATM38 | Mathematical Models in Biology, 6 ECTS credits. /Matematiska modeller i biologi/ |
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Prel. scheduled
hours: 60 |
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Area of Education: Science Subject area: Mathematics |
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| Advancement level
(A-D): C
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| Aim: Mathematical modelling of processes in nature consist of three steps: a) formulation of a model on the basis of observed experimental relations b) mathematical analysis of the model: mainly solving the differential or difference equations that describe the process c) interpretation of the mathematical answers During the course participants will learn mathematics needed for building a model as well as modelling itself. Mathematics involves methods of theory of dynamical systems and of theory of linear partial differential equations. The course start with building a model for chemostat, a devise used for industrial breeding of bacteria cultures. Careful analysis of this model creates a conceptual basis for understanding more complicated dynamical systems. This mathematics is used for formulating and solving basic models used in population dynamics, epidemiology and morphogenesis. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Mathematics corresponding to TATM 72 Analysis A, TATM 73 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. |
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| Organisation: This course consists of lectures. problem solving sessions and of a project report. |
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| Course contents: Elementary methods of solving 1-st and 2-nd order ordinary differential equations. Elements of theory of dynamical systems: equilibrium points and their stability, nullclines, integrals of motion, phase space picture. Phase plane diagram for the chemostat. Quadratic models for interacting populations and epidemics. Linear and nonlinear difference equations. Logistic equation. Solving diffusion type equations through separation of variables. Fourier series. Boundary value problems. Population dispersal models based on diffusion. A model for aggregation of cellular slime molds. Conditions for diffusive instability and a chemical basis for morphogenesis. |
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| Course literature: Edelstein - Keshet, L. Mathematical Models in Biology ISBN 0-07-554850-6 |
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| Examination: | |||
| Written examination Written reports |
3 p 1 p |
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Course language is Swedish. Department offering the course: MAI. Director of Studies: Arne Enqvist Examiner: Stefan Rauch Link to the course homepage at the department Course Syllabus in Swedish |
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