### Course: Mathematics i

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 Course title Mathematics i KMD/MA1-E Lecture + Seminary Bachelor not specified Winter 5 Czech Compulsory, Optional Face-to-face Course does not contain work placement None The course is available to visiting students
Lecturer(s)
• Mlýnek Jaroslav, doc. RNDr. CSc.
• Bittnerová Daniela, RNDr. CSc.
Course content
A. Definitions of mapping and function 1. Introduction - used symbols, notations. Basic terms of sententional calculus. Number sets. 2. Mapping, basic terms (domain of definition, image of mapping, types of mapping). Real function, basic properties of functions (monotony, bounded functions, even, odd). 3. Inverse function. Basic elementary functions (including cyclometric). 4. Other functions (absolute value, signum, entire function, Dirichlet's function). Real sequences. B. Differential calculus 5. Limit of sequence (finite, infinite), theorems about limit, calculation of limit, number e. 6. Limit function, one-sided limits, limits at infinite points. Continuity, properties of continuous functions. 7. Derivative, geometric applications, tangent line to a function. Calculation of derivative, derivative of a composite function, derivative of an inverse function. 8. L'Hospital's rule. Monotony, local and global extreme of a function. 9. Convexity, concavity, point of inflexion. Applications of derivatives to studying of graph of a function. 10. Differential of a function. Taylor's formula. C. Integral calculus 11. Primitive function and indefinite integral. Basic rules, method per partes, substitution method. 12. Integration by partial fractions. 13. Riemann definite integral, Newton-Leibniz's theorem. Infinite integral. 14. Number series, criterions of convergence, absolute convergence.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
• Class attendance - 56 hours per semester
• Preparation for credit - 26 hours per semester
• Semestral paper - 10 hours per semester
• Home preparation for classes - 28 hours per semester
Learning outcomes
Basic mathematical concepts. Foundations of the differential calculus, finite and infinite limits in finite and infinite points, including left-hand and right-hand limits. Derivation and its applications, specially to continuity of a function. Basis of integral calculus and Riemann integral. Number progressions. All items regarding to economic applications.
Basic knowledge of higher mathematics.
Prerequisites
Knowledge of mathematics at the high school level

Assessment methods and criteria
Combined examination

Credit: knowledge of mathematics at the high school level, regular attendance, passing of three tests
Recommended literature
• Bittnerová, D. - Plačková, G.:. Louskáček 1 - Diferenciální počet funkcí jedné reálné proměnné (Sbírka úloh). Liberec, TUL 2006, 2007..
• Bittnerová, D. - Plačková, G.:. Louskáček 2 - Integrální počet funkcí jedné reálné proměnné..
• Jirásek, F. - Kriegelstein, E. - Tichý, Z.:. Sbírka řešených příkladů z matematiky I.. Praha, 1990.
• Kaňka, M. - Henzler J.:. Matematika 2, Ekopress.. Praha, 2003. ISBN 80-86119-77-7.
• Klůfa, J. - Coufal, J.:. Matematika 1, Ekopress.. Praha, 2003. ISBN 80-86119-76-9.
• Nekvinda, M. - Vild, J.:. Matematické oříšky I. Liberec, 2000. ISBN 80-7083-762-4.
• Rektorys, K. a další:. Přehled užité matematiky.. Praha, Prometheus, 2000. ISBN 80-85849-92-5.
• Vild, J. - Říhová, H.:. Diferenciální kalkul F1.. Liberec, 2002. ISBN 80-7083-552-4.
• Vild, J. - Říhová, H.:. Integrální kalkul F1.. Liberec, 2005. ISBN 80-7083-587-7.

 Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science, Humanities and Education Study plan (Version): Recreology (20) Category: Physical education and sport - Recommended year of study:-, Recommended semester: Winter