Course: Mathematics 3

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Course title Mathematics 3
Course code KMA/M3
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 3
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)
  • Fišer Jiří, RNDr. Ph.D.
  • Pastor Karel, doc. Mgr. Ph.D.
Course content
ORDINARY DIFFERENTIAL EQUATIONS (ODEs) 1. Introduction. Motivation. 2. First order ODEs, Cauchy initial problem, existence and uniqueness of solutions, direction field. 3. Elementary methods: separable ODEs. 4. Elementary methods: substitutions. 5. Linear first order ODEs, Method of variation of parameters. 6. Linear second order ODEs. 7. Homogeneous linear second order ODEs. 8. Non-homogeneous linear second order ODEs: method of variation of parameters. 9. Non-homogeneous linear second order ODEs: method of variation of undetermined coefficients. DIFFERENCE EQUATIONS 10. First order difference equations, linear first order difference equations. 11. Linear n-th order difference equations: homogeneous equations with constant coefficients. 12. Linear n-th order difference equations: non-homogeneous equations with constant coefficients - method of undetermined coefficients.

Learning activities and teaching methods
Monologic Lecture(Interpretation, Training)
  • Attendace - 26 hours per semester
  • Preparation for the Course Credit - 20 hours per semester
  • Preparation for the Exam - 40 hours per semester
Learning outcomes
Basic skills in the treatment of ordinary differential and difference equations.
Comprehension Basic skills in the treatment of ordinary differential and difference equations.
Prerequisites
Differential calculus of functions of one and several variables, integration on the real axis.
KMA/M2
----- or -----
KMA/M2N

Assessment methods and criteria
Mark, Oral exam, Written exam

Credit: the student has to obtain at least half of the possible points in written test. Exam: the student has to understand the subject.
Recommended literature
  • A. Prágerová. (1971). Diferenční rovnice. SNTL, Praha.
  • J. Kojecká, M. Závodný. (2004). Příklady z diferenciálních rovnic I. Skriptum UP Olomouc.
  • J. Kuben. (1991). Obyčejné diferenciální rovnice. VA Brno.
  • S. N. Elaydi. (1999). An Introduction to Difference Equations. Springer, New York.
  • V. I. Arnoľd. (1992). Ordinary Differential Equations. Springer Berlin.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Statistics (2015) Mathematics courses 2 Winter
Faculty of Science Mathematics-Economics of Banking / Insurance Systems (1) Mathematics courses 2 Winter