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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 Seminar Mathematics 1 (MC1-M) aims at equalizing the entry level of mathematical knowledge at students and acquiring practical skills in solving the examples related to the subject lectured in the subject Mathematics 1. Examples and problems related to the field of study will be given. During the semester, the students have to solve at least two tests, the successful completion of which is a necessary condition for obtaining a credit. 1. Repetition of secondary school mathematics - equations, inequalities, graphs of functions. 2. Repetition of secondary school mathematics - combinatorics. Propositional calculus, naive set theory. 3. Sequence of real numbers, limits. Boolean logic. 4. Continuity and limits of functions. Compositions of functions, inverse function. 5. Asymptotes of the graph of function, especially of rational function. Concept of derivative. Boolean algebra. 6. Properties of the derivative, derivative of composite 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. Investigation of functions. Determinants. 10. Primitive function, indefinite integral, integration by parts and by substitution. 11. Integration of rational functions and some irrational functions. 12. Riemann integral, essential properties of definite integral. Relationship between definite and indefinite integra, Newton-Leibniz theorem. 13. Geometrical and physical applications of Riemann integral. 14. Time reserve, repetition.
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Learning activities and teaching methods
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Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Practicum, E-learning, Students' portfolio
- Class attendance
- 56 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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Student's performance analysis, Systematické pozorování studenta, Written assignment, Test
Credit: succesful passing of tests, active participation on seminars.
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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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