Course: Ordinary Differential Equations 1

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Course title Ordinary Differential Equations 1
Course code KMA/ODR1
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Staněk Svatoslav, prof. RNDr. CSc.
Course content
1. Computing methods for differential equations of the first order. 2. Fundamentals of differential equations, autonomous systems, the relation of a single equation to a system. 3. Local existece and uniqueness theorems for the initial value problems, the Gronwall lemma. 4. Extending the solution, complete solution, global existece and uniqueness theorems for initial value problems, differential inequalities, existence on a half-line. 5. Systems of linear differential equations (superposition, fundamental solution, the Wronskian, the Jacobi formula, variation of constants formula, general solution). 6. Linear differential equation of the n-th order. 7. Systems of linear differential equations with constant coefficients, structure of the solution. 8. Linear differential equation of the n-th order with constant coefficients.

Learning activities and teaching methods
Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Homework for Teaching - 20 hours per semester
  • Preparation for the Exam - 50 hours per semester
Learning outcomes
Understand local and global properties of solution to ordinary differential equations and their systems.
Comprehension Understand local and global properties of solution to ordinary differential equations and their systems.
Prerequisites
Knowledge of differential and integral calculus, linear algebra and basic information from functional analysis.

Assessment methods and criteria
Oral exam, Written exam

Credit: active participation, homework. Exam: written test, the student has to understand the subject and be able to prove principal results.
Recommended literature
  • J. Kalas, M. Ráb. (1995). Obyčejné diferenciální rovnice. Brno.
  • Kurzweil, J. (1978). Obyčejné diferenciální rovnice: úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. Praha: SNTL - Nakladatelství technické literatury.
  • M. Greguš, M. Švec, V. Šeda. (1985). Obyčajné diferenciálne rovnice. Alfa, SNTL.
  • Ráb, M. (1998). Metody řešení obyčejných diferenciálních rovnic. MU Brno.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Discrete Mathematics (2015) Mathematics courses 1 Winter