Course objectives:
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The goal of this course is to acquaint students with use of differential equations (mainly partial) in mathematical models in biology and ecology.
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Requirements on student
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The students should be able to combine a study of qualitative properties of differential equations (mainly partial) with relevant problems in biology and ecology.
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Content
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Simple population models with diffusion. Interpretation of boundary conditions. Influence of diffusion and boundary conditions to stationary states and their stability. Fundamentals of bifurcation theory. Models of chemical (biochemical) reactions. Simple reaction-diffusion systems, diffusion driven instability, arrising of spation patterns. Interpretation in models of morphogenesis.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for an examination (30-60)
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52
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Contact hours
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26
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Total
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78
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
Knowledge of ordinary differential equations, basic imagination on partial differential equations and knowledge of basic notions of functional analysis. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
After succesfull finishing this course, students will have a basic survey about a possible influence of diffusion and boundary conditions in population models and models of chemical (biochemical) reactions. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture supplemented with a discussion |
Interactive lecture |
Self-study of literature |
Individual study |
One-to-One tutorial |
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