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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
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.