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Applied differential equations - NMMA706

Title:	Aplikované diferenciální rovnice
Guaranteed by:	Department of Software and Computer Science Education (32-KSVI)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2025 to 2025
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, C+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

Guarantor:	doc. RNDr. Tomáš Bárta, Ph.D.
Teacher(s):	doc. RNDr. Tomáš Bárta, Ph.D. Karolína Korvasová, M.Sc., Dr. rer. nat.

Opinion survey results SS schedule Noticeboard

Annotation -

Existence, uniqueness, basic properties of solutions to ODE's. Solution methods to selected ODE's. Qualitative analysis. Applications: derivation and analysis of basic models (biology, physics, economy).

Last update: Kaplický Petr, doc. Mgr., Ph.D. (01.06.2017)

Course completion requirements -

The credit for exercises is awarded for elaborating homework.

The credit from exercises is required to participate at the exam.

The written exam contains material from both the lectures and the practicum.

Last update: Korvasová Karolína, M.Sc., Dr. rer. nat. (07.05.2026)

Literature -

I. I. Vrabie: Differential equations : an introduction to basic concepts, results, and applications. World Scientific, 2004.

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: Kaplický Petr, doc. Mgr., Ph.D. (01.06.2017)

Requirements to the exam -

Ability to solve problem similar to those solved at the exercises, knowledge of the theory presented in the lecture, understanding. Details at the web page of the lecturer.

Last update: Korvasová Karolína, M.Sc., Dr. rer. nat. (13.05.2026)

Syllabus -

1. Systems of ODE -- basic examples and applications.

2. Existence, uniqueness and further properties of solutions.

3. Systems of linear equations, variation of constants,

matrix exponential.

4. Asymptotic behavior, stability.

Last update: Korvasová Karolína, M.Sc., Dr. rer. nat. (13.05.2026)

Entry requirements -

Differential and integral calculus in one variable.

Basic linear algebra (matrix theory in particular).

Last update: Pražák Dalibor, doc. RNDr., Ph.D. (01.05.2018)