Mathematical modeling in environmental science WF-OB-MODM
- https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3 (term 2021/22_Z)
- https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3 (term 2022/23_Z)
- https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3 (term 2023/24_Z)
- https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3 (term 2024/25_Z)
Modelling in biology. Mathematics as an language for natural sciences. Description of time and space in mathematical models. Statictical or empirical models. Vollenweide'sr model as an example. Habitat models on example of scenariuos Vistulla valley transformations. Model LARCH and RAMAS. NetLogo as a usful programming tool. Population growth - linear, exponential and logistic model. Deterministic chaos. Stochastic models of small populations. Stability - its mathematical formulation and ecological interpretations. Are ecological systems stable? Stability and complexity question. Dynamics of two competing population. Predator-prey system dynamics. Oscillations and limit cycles. Models of matter cycling in ecosystems. Phosporus cycling in a lake as an example of ecosystem's functioning model. Forest dynamics models. Cellural automata. Individual-based modeling and its differences with classical modeling. Fractal modelling - unitary and modular organisms. Speciation and extinction of species.
(in Polish) E-Learning
(in Polish) Grupa przedmiotów ogólnouczenianych
Subject level
Learning outcome code/codes
Type of subject
Course coordinators
Learning outcomes
Knowledge
EF1 - Student knows basic models used in ecology
Abilities
EK2 - Student is able to build simple model of an ecological process.
Competence
EK3 - Student knows that application of maqthematical and compouters methods is useful in ecology and nature protection.
Assessment criteria
Score on basis of the end test.
Bibliography
Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka
Bodnar M. 2008. Zbiór zadań z matematyki dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa
Czarnowski D. S., Romanowski J. M., Stiepanowa N. W. 1974. Co to jest biofizyka matematyczna. PWN.
Foryś U. 2005. Matematyka w biologii. Wydawnictwa Naukowo-Techniczne, Warszawa.
Murray J.D. 1989. Mathematical biology. Springer-Verlag.
Murray J. D. 2006. Wprowadzenie do biomatematyki. Wydawnictwo Naukowe PWN, Warszawa.
Uchmański J. 1992. Klasyczna ekologia matematyczna.PWN.
Uchmański J. 2022. Modele matematyczne w ekologii. Wydawnictwa UKSW.
Wit R. 1994. Wykłady o modelowaniu w fizyce medycznej. Uniwersytet Jagielloński.
Wrzosek D. 2008. Matematyka dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa
|
Term 2021/22_Z:
Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka |
Term 2022/23_Z:
Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka |
Term 2023/24_Z:
Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka |
Term 2024/25_Z:
Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka |
Notes
|
Term 2021/22_Z:
High school level of mathematics |
Term 2022/23_Z:
High school level of mathematics |
Term 2023/24_Z:
High school level of mathematics |
Term 2024/25_Z:
High school level of mathematics |
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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