## UIMOIBP004 Mathematics I

Faculty of Philosophy and Science in Opava
Winter 2021
Extent and Intensity
2/3/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Luděk Cienciala, Ph.D. (lecturer)
doc. RNDr. Luděk Cienciala, Ph.D. (seminar tutor)
RNDr. Radka Poláková, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Luděk Cienciala, Ph.D.
Institute of Computer Science - Faculty of Philosophy and Science in Opava
Timetable
Mon 9:45–11:20 B1
• Timetable of Seminar Groups:
UIMOIBP004/A: Wed 8:05–10:30 B2, R. Poláková
UIMOIBP004/B: Wed 11:25–13:50 B2, R. Poláková
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The language of mathematics, introduction to logic. Function, function graph. Limit and continuity of a function, limit of a sequence. Differential calculus of a function of one real variable, derivation, derivation of higher orders, differential of a function. Indefinite integral. Definite integral.
Learning outcomes
Students will be able to:
- define terms discussed in the course;
- analyze the basic functions;
- determine the limit or derivative of simple functions.
Syllabus
• 1. Language of mathematics, introduction to logic.
• 2. Concept of function, basic properties of function, elementary functions, definition field of function, determination of basic properties of function.
• 3. Graph of a function.
• 4. Limit and continuity of a function, limit of a sequence.
• 5. Differential calculus of a function of one real variable, derivation, derivation of higher orders, differential of a function. Application of derivation, l´Hospital's rule, geometric meaning of derivation of a function at a point.
• 6. The course of the function.
• 7. Indefinite integral, methods of calculation of indefinite integral, integration by substitution method, integration by per partes method, integration of rational function, integration of irrational function, integration of trigonometric functions, trigonometric substitution.
• 8. Definite integral, geometric application of definite integral, content of a figure, volume of a rotating body, length of an arc of a plane curve, content of a rotating surface.
Literature
required literature
• CIENCIALA Luděk. Matematika I. Skripta. 97 stran. Slezská univerzita v Opavě, 2017
recommended literature
• Brožková, A. Cvičení z matematické analýzy II. pe. info
• VOPĚNKA, Petr. Nová infinitní matematika IV: Staronový diferenciální počet. Praha: Univerzita Karlova, nakladatelství Karolinum, 2015. ISBN 9788024629841
• WILLERS, Michael. Algebra bez (m)učení: od arabských matematiků k tajným šifrám: matematika v každodenním životě : fascinující čísla a rovnice. Praha: Grada, 2012. ISBN 978-802-4741-239
• VOPĚNKA, Petr. Nová infinitní matematika II: Nová teorie množin a polomnožin. Praha: Univerzita Karlova, nakladatelství Karolinum, 2015. ISBN 978-802-4629-865
• Cienciala, L., Ciencialová, L. Teorie grafů a grafové algoritmy. Slezská univerzita v Opavě, 2014. ISBN 978-80-7510-060-3. info
• Děmidovič Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 2003. ISBN 80-7200-587-1. info
• ČERNÝ,I., ROKYTA, M. Differential and integral calculus of one real variable. Praha : Karolinum, 1998. ISBN 80-7184-661-9. info
• Brožková, A. Cvičení z matematické analýzy I. Pedagogická fakulta Ostravské univerzity, 1995. info
Teaching methods
Lecture, tutorial
Assessment methods
Credit:
Compulsory participation in seminars min. 75%.
The student writes two credit tests scored a maximum of 30 points for each. He also submits solutions to five homework assignments. He gets a maximum of 8 points for each homework. 50 points are required to obtain the credit. The points obtained during the semester are multiplied by a coefficient of 0.4 and rounded up. The points recalculated in this way are added to the test.
Exam:
The student can get a maximum of 60 points from the exam test. He needs 30 points to succeed. To determine the mark from the exam, the points obtained in the semester from the credit tests and the exam test are added up. The maximum number of points is 100.
Language of instruction
Czech