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Lecturer(s)
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Soudský Filip, RNDr. Ph.D.
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Břehovský Jiří, Mgr. Ph.D.
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Course content
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Lectures: 1. Sets, numbers, logic, proofs in mathematics, concept of a mapping and a function. Supremum and infimum. 2. Compositions of functions, inverse functions, real functions and their characteristics, plane curves. 3. Sequences of real numbers, limits. 4. Continuity and limits of functions. 5. Asymptotes of the graph. Concept of a derivative. 6. Derivative and its characteristics, derivative of a composed function. 7. Differential and its applications. 8. Theorems about continuous functions, the mean value theorems, l´Hospital rule. 9. Meaning of the first and second derivative, inflexion, relative and absolute extrema, asymptotes, investigation of functions. 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. Practice: 1. Sets, numbers, logic, proofs in mathematics, mapping and function, supremum and infimum. 2. Compositions of functions, inverse functions, real functions, plane curves. 3. Sequences of real numbers, limits. 4. Continuity and limits of functions. 5. Asymptotes of the graph. Derivative. 6. Repetition. 7. Differential. 8. Theorems about continuous functions, the mean value theorems, l´Hospital rule. 9. Investigation of functions. 10. Primitive function, indefinite integral, integration by parts and by substitution. 11. Integration of rational functions and some irrational functions. 12. Riemann integral. 13. Geometrical and physical applications of Riemann integral. 14. Repetition.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 70 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.
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 proper integral).
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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
Credit: succesful pass of two credit tests, active participation on seminars. Exam: combined exam, it consists of the written theoretical part and practical computations. The results of the tests will be taken into account in the exam.
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Recommended literature
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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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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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Rektorys, K. a další:. Přehled užité matematiky.. Praha, Prometheus, 2000. ISBN 80-85849-92-5.
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