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Lecturer(s)
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Mlýnek Jaroslav, doc. RNDr. CSc.
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Knobloch Roman, Mgr. Ph.D.
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Břehovský Jiří, Mgr. Ph.D.
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Course content
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Lectures: A. Differential calculus. 1. Number sets. Mapping, basic terms (domain of definition, image of mapping, types of mapping). 2. Real function of one variable. Basic elementary functions. Basic properties of functions and operations with functions. 3. Limit and continuity of functions. Calculation of limits. Properties of continuous function. 4. Derivative, geometric geometrical meaning, tangent to a function. Calculation of derivative, derivative of a composite function. 5. Relationship between the derivative of a function and its progression (monotonicity, local extremes, convexity and concavity, inflection points). Asymptotes. Investigation of the progress of simpler functions. 6. Number series, convergence, divergence, convergence criteria, absolute convergence. B. Integral calculus. 7. Primitive function and indefinite integral. Methods of integration (per partes, substitution method). 8. Riemann definite integral and its calculation. Newton-Leibnitz theorem. C. Combinatorics 9. Combinatorial rules, variations and combinations without and with repetition, permutations. 10. Application of combinatorics terms for solution of problems, relation to probability calculations. D. Linear algebra 11. Arithmetic n-dimensional vector space, linear dependence/independence of vectors, basis and dimension of vector space. 12. Matrices, introduction, properties and operations with matrices, matrix rank, singular and regular matrices. 13. Systems of linear algebraic equations, solution of a system of linear algebraic equations, Frobenius theorem. Gaussian elimination method. 14. Reserve.
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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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Basic mathematical terms. Function of one real variable. Fundamentals of differential calculus. Limit and continuity of a function. Derivation and its applications, progression of a function. Fundamentals of integral calculus, indefinite and Riemann integral. Numerical series. Fundamentals of combinatorics. Fundamentals of linear algebra, vector space. Matrix operations, solving systems of linear algebraic equations. All taking into account economic applications.
Basic knowledge of higher mathematics.
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Prerequisites
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Knowledge of mathematics at the high school level
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Assessment methods and criteria
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Combined examination
Credit: knowledge of mathematics at the high school level, regular attendance, passing of three tests
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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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Klůfa, J. Matematika pro bakalářské studium. Ekopress, Praha, 2019. ISBN 978-80-87865-53-8.
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