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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)
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The credit for exercises is awarded for elaborating homework.
The credit from exercises is required to participate at the exam.
The exam consists of a written computational part (test) and oral theoretical part.
Students failing in the test are not allowed to continue with the oral part. Students failing in the oral part must go through both parts (written and oral) in their next attempt. Last update: Bárta Tomáš, doc. RNDr., Ph.D. (02.03.2021)
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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)
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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: Bárta Tomáš, doc. RNDr., Ph.D. (23.05.2019)
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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: Kaplický Petr, doc. Mgr., Ph.D. (05.06.2017)
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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)
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