SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Applications of Differential Equations in Biology - NMMA466
Title: Aplikace diferenciálních rovnic v biologii
Guaranteed by: Department of Software and Computer Science Education (32-KSVI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Is provided by: NMMA706
Additional information: http://msekce.karlin.mff.cuni.cz/~prazak/vyuka/706/
Guarantor: Karolína Korvasová, M.Sc., Dr. rer. nat.
Class: M Bc. OM
M Bc. OM > Doporučené volitelné
Classification: Mathematics > Real and Complex Analysis, Topology and Category
Annotation -
We derive some biological models (e.g. predator-prey models, epidemiological models, population models) and apply results of the theory of ordinary differential equations to these models.
Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)
Course completion requirements -

The course is concluded with an oral exam which can be waived on the basis of ongoing homework assignments.

Last update: Bárta Tomáš, doc. RNDr., Ph.D. (23.05.2019)
Literature -

D. S. Jones, B. D. Sleeman: Differential equations and mathematical biology, Chapman & Hall, 2003.

J. D. Murray: Mathematical biology I: an introduction, Springer, 2002.

Last update: Bárta Tomáš, doc. RNDr., Ph.D. (23.05.2019)
Requirements to the exam -

Knowledge of the theory presented in the lectures, details at the web page of the lecturer.

Last update: Bárta Tomáš, doc. RNDr., Ph.D. (23.05.2019)
Syllabus -

1. Population models (Malthusian growth model, model with capacity of environment, Lotka--Volterra predator-prey model, Holling--Tanner, Gause's model with a shelter).

2. Epidemiologic models (SIR, SLIAR, SIR with space variable).

3. Replicator dynamics.

Last update: Bárta Tomáš, doc. RNDr., Ph.D. (10.05.2018)
Entry requirements -

The course is a good supplement to the course Ordinary differential

equations NMMA333. We recommend the students who are not acquainted with

basic theory of ordinary differential equations to attend the course

NMMA706 instead.

Last update: Pyrih Pavel, doc. RNDr., CSc. (04.05.2018)
 
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