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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Course content
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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.
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Learning activities and teaching methods
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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
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Learning outcomes
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Basic skills in the treatment of ordinary differential and difference equations.
Comprehension Basic skills in the treatment of ordinary differential and difference equations.
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Prerequisites
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Differential calculus of functions of one and several variables, integration on the real axis.
KMA/M2N
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Assessment methods and criteria
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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.
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Recommended literature
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A. Prágerová. (1971). Diferenční rovnice. SNTL, Praha.
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J. Kojecká, M. Závodný. (2004). Příklady z diferenciálních rovnic I. Skriptum UP Olomouc.
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J. Kuben. (1991). Obyčejné diferenciální rovnice. VA Brno.
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S. N. Elaydi. (1999). An Introduction to Difference Equations. Springer, New York.
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V. I. Arnoľd. (1992). Ordinary Differential Equations. Springer Berlin.
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