### Course: Mathematics I

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 Course title Mathematics I KMD/MA1-M Lecture + Lesson Bachelor not specified Winter 6 Czech Compulsory Face-to-face Course does not contain work placement None The course is available to visiting students
Lecturer(s)
• Knobloch Roman, Mgr. Ph.D.
• Finěk Václav, doc. RNDr. Ph.D.
• Bittnerová Daniela, RNDr. CSc.
• Břehovský Jiří, Mgr. Ph.D.
• Bittner Václav, Mgr. Ph.D.
Course content
Lectures: 1. Sets, numbers, inequality, supremum and infimum, logic, proofs in mathematics, functions. 2. Compositions of functions, inverse functions, mathematical functions and their properties, plane curve. 3. Sequences of real numbers, limits. 4. Continuity and limits of functions. 5. Derivatives and differentials. 6. Repetition. 7. Theorems about continuous functions, the mean value theorems, l´Hospital rule. 8. Monotone functions, convex and concave functions, meaning of the first and second derivative, inflexion, relative and absolute extrema, asymptotes, investigation of functions. 9. Riemann integral. 10. Primitive integral, integration by parts and by substitution, the fundamental theorems of integral calculus. 11. Integration of rational and some irrrational functions. 12. Integration of rational and some irrrational functions. 13. Geometric applications of Riemann integral, basic numerical methods for nonlinear equations and basic numerical quadratures. 14. Repetition. Practice: 1. Sets, numbers, inequality, supremum and infimum, logic, proofs in mathematics, functions. 2. Compositions of functions, inverse functions, mathematical functions and their properties, plane curve. 3. Sequences of real numbers, limits. 4. Continuity and limits of functions. 5. Derivatives and differentials. 6. Repetition. 7. Theorems about continuous functions, the mean value theorems, l´Hospital rule. 8. Monotone functions, convex and concave functions, meaning of the first and second derivative, inflexion, relative and absolute extrema, asymptotes, investigation of functions. 9. Investigation of functions. 10. Riemann and primitive integral, integration by parts and by substitution, the fundamental theorems of integral calculus. 11. Integration of rational and some irrrational functions. 12. Integration of rational and some irrrational functions. 13. Geometric applications of Riemann integral, basic numerical methods for nonlinear equations and basic numerical quadratures. 14. Repetition.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
• Class attendance - 70 hours per semester
• Preparation for credit - 28 hours per semester
• Preparation for exam - 42 hours per semester
• Home preparation for classes - 40 hours per semester
Learning outcomes
The subject represents an introduction to calculus (differential and integral) of function of one real variable.
Calculus (differential and integral) of function of one real variable.
Prerequisites
Knowledge of secondary school mathematics.

Assessment methods and criteria
Combined examination

Credit: Active participation on seminars + tests. Exam: writtten.
Recommended literature
• Brabec, J. - Martan, F. - Rozenský, Z.:. Matematická analýza I. Praha, SNTL, 1985.
• Budinský, B. - Charvát, J.:. Matematika I [skriptum ČVUT fakulta stavební]. Praha, 2000.
• Mezník, I. - Karásek, J. - Miklíček, J. Matematika 1 pro strojní fakulty. Praha, SNTL, 1992.
• Nekvinda, M. - Vild, J.:. Matematické oříšky I. Liberec, 2000. ISBN 80-7083-762-4.
• Nekvinda, M. - Vild, J.:. Náměty pro samostatné referáty z matematiky. Liberec, 1995.
• Nekvinda M.:. Matematika I [Skriptum TUL]. Liberec, 1999.
• Rektorys, K. a další. Přehled užité matematiky. Praha, 1995.

 Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Information Technology (2013) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Applied Sciences in Engineering (2016) Category: Special and interdisciplinary fields 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Applied Sciences in Engineering (2019) Category: Special and interdisciplinary fields 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Mechatronics, Informatics and Interdisciplinary Studies Study plan (Version): Informatics and Logistics (2015) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter