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
Opinion survey results   Examination dates   SS schedule   Noticeboard   
Annotation -
Last update: doc. RNDr. Pavel Pyrih, CSc. (04.05.2018)
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.
Course completion requirements -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (23.05.2019)

The course is concluded with an oral exam which can be waived on the basis of ongoing homework assignments.
Literature -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (23.05.2019)

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

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

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

Knowledge of the theory presented in the lectures, details at the web page of the lecturer.
Syllabus -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (10.05.2018)

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

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.