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Lecturer(s)
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Soudský Filip, RNDr. Ph.D.
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Course content
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The subject Mathematics 1 (MP1-M) represents an introductory course of differential and integral calculus of the function of one real variable and an introduction of discrete mathematics and linear algebra. Lectures: 1. Propositional calculus, naive set theory, proofs in mathematics. Essential number sets, supremum theorem. 2. Concept of a mapping, function, composition of functions, inverse function, inverse goniometric functions. 3. Sequences of real numbers, limits, number e. Introduction into Boolean logic. 4. Continuity and limit of function. 5. Asymptotes of the graph. Concept of a derivative, its geometrical and physical interpretation. Boolean algebra. 6. Derivative and its characteristics, derivative of a composed function, inverse function, logarithmic derivative. 7. Derivative of higher order. Differential and its use. Derivative of the function given parametrically, implicitly, in polar coordinates. Systems of linear algebraic equations. 8. Properties of continuous functions on the restricted closed interval, the mean value theorems, l´Hospital rule. 9. Meaning of the first and second derivative, inflexion, relative and absolute extrema, asymptotes, investigation of functions. Matrices and determinants. 10. Primitive function and indefinite integral, integration by parts and by substitution. 11. Integration of rational functions and some irrational functions. 12. Riemann integral and its characteristics, Newton-Leibniz theorem. 13. Geometrical and physical applications of Riemann integral. 14. Time reserve, summary.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Lecture, E-learning
- Class attendance
- 56 hours per semester
- Home preparation for classes
- 60 hours per semester
- Preparation for exam
- 34 hours per semester
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Learning outcomes
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The subject represents an introduction to calculus (differential and integral) of function of one real variable and to linear and Boolean algebra, too.
A student masters calculus (differential and integral) of function of one real variable, he is able to use the theory for solving practical problems (extrema of functions, properties of continuous functions on the interval, essential methods of integration, applications of the definite integral). A student will be able to solve linear algebraic equations by means of Gauss elimination method and determinants, too.
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Prerequisites
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Secondary school mathematics.
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Assessment methods and criteria
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Combined examination, Test
It is necessary to pass the credit from the subject MC1-M prior to the exam.
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Recommended literature
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Bittnerová, D. - Plačková, G.:. Louskáček 1, 2. (skriptum TUL). Liberec, 2013.
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Brabec, J. - Martan, F. - Rozenský, Z.:. Matematická analýza I. Praha, SNTL, 1985.
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Budinský, B., Charvát, J.:. Matematika 1 [skriptum ČVUT fakulta stavební]. Praha, 2000.
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Černý, I. Úvod do inteligentního kalkulu. Praha, 2002.
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Hardy, G. H. Course of Pure Mathematics. Courier Dover Publications, 2018. ISBN 9780486822358.
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Mezník, I. , Karásek, J., Miklíček, J.:. Matematika I pro strojní fakulty. SNTL, Praha, 1992.
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Nekvinda, M. - Vild, J.:. Matematické oříšky I. Liberec, 2000. ISBN 80-7083-762-4.
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Nekvinda, M. - Vild, J.:. Náměty pro samostatné referáty z matematiky. Liberec, 1995.
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Nekvinda, M.:. Matematika I. Liberec TU, 1999.
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Nešetřil, J. - Matoušek, J. Kapitoly z diskrétní matematiky. Praha, 2000.
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Rektorys, K. a další:. Přehled užité matematiky.. Praha, Prometheus, 2000. ISBN 80-85849-92-5.
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