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Lecturer(s)
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Němec Jiří, prof. RNDr. DrSc.
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Course 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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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, One-to-One tutorial, Individual study, Self-study of literature
- Contact hours
- 26 hours per semester
- Preparation for an examination (30-60)
- 52 hours per semester
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| prerequisite |
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| Knowledge |
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| Knowledge of ordinary differential equations, basic imagination on partial differential equations and knowledge of basic notions of functional analysis. |
| learning outcomes |
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| 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. |
| teaching methods |
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| Lecture supplemented with a discussion |
| Interactive lecture |
| Self-study of literature |
| Individual study |
| One-to-One tutorial |
| assessment methods |
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| Combined exam |
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Recommended literature
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Allman, Elizabeth Spencer; Rhodes, John A. Mathematical models in biology : an introduction. 1st pub. New York : Cambridge University Press, 2004. ISBN 0-521-52586-1.
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Britton, N. F. Reaction-Diffusion Equations and Their Applications to Biology. Academic Press, 1986.
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Cantrell, R. S.; Cosner, C. Spatial ecology via reaction-diffusion 20quations. 2003. ISBN 0-471-493201-5.
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Murray, J. D. Mathematical biology. 2nd ed. corr. Berlin : Springer, 1993. ISBN 3-540-57204-X.
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