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Lecturer(s)
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Bittner Václav, Mgr. Ph.D.
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Knobloch Roman, Mgr. Ph.D.
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Course content
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Lectures: A) Introduction to the study of ordinary differential equations 1) Basics of ODR theory; ODR1 2) Linear ODR of n-th order 3) ODR1 systems B) Introduction to differential and integral calculus of functions of more real variables 4) Functions of more variables (basic concepts, function limits, continuity, partial derivatives) 5) Directional derivation; higher order partial derivatives; differential of function and Taylor polynomial 6) Extremes of functions of more variables 7) Implicit function 8) Multidimensional integral I 9) Multidimensional integral II 10) Curve integral; Vector operators and potential 11) Surface integral I 12) Surface integral II C) Introduction to the study of number and function series 13) Number series (basic terms, infinite series, convergence criteria) 14) Function series (convergence types, basic properties, power series) Exercises: The knowledge from the lecture is practiced. Examples of applications of knowledge in the fields of Biomedical Engineering and Radiology are included. Available software applications are used.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
- Semestral paper
- 15 hours per semester
- Preparation for credit
- 30 hours per semester
- Home preparation for classes
- 60 hours per semester
- Preparation for exam
- 50 hours per semester
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Learning outcomes
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The subject represents an introduction to differential and integral calculus of function of more (especially two) real variables, an essential course of differential equations and introduction to number and function series.
Mastering essentials of differential calculus of function of more (especially two) real variables, ordinary differential equations, essentials of number and function series.
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Prerequisites
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Knowledge of mathematics at the high school level, knowledge of AMR1
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Assessment methods and criteria
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Combined examination
Credit: Active participation on seminars and written tests. Exam: written exam, consists of the practical examples and the theoretical part. The evaluation on seminars will be taken into account in the exam.
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Recommended literature
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Bittnerová, D. - Plačková, G.:. Louskáček 1 - Diferenciální počet funkcí jedné reálné proměnné (Sbírka úloh). Liberec, TUL 2006, 2007..
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Bittnerová, D. - Plačková, G.:. Louskáček 2 - Integrální počet funkcí jedné reálné proměnné..
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Kaňka, M. - Henzler J.:. Matematika 2, Ekopress.. Praha, 2003. ISBN 80-86119-77-7.
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Klůfa, J. - Coufal, J.:. Matematika 1, Ekopress.. Praha, 2003. ISBN 80-86119-76-9.
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Vild, J. - Říhová, H.:. Diferenciální kalkul F1.. Liberec, 2002. ISBN 80-7083-552-4.
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Vild, J. - Říhová, H.:. Integrální kalkul F1.. Liberec, 2005. ISBN 80-7083-587-7.
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