UIBUC03 Mathematics I

Faculty of Philosophy and Science in Opava
Winter 2021
Extent and Intensity
2/3/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Luděk Cienciala, Ph.D. (lecturer)
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:
UIBUC03/A: Wed 8:05–10:30 B2, R. Poláková
UIBUC03/B: Wed 11:25–13:50 B2, R. Poláková
Prerequisites
Mathematics in the range secondary school curriculum.
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 aim of the course is to acquaint students with the basic concepts of mathematical analysis.
Syllabus
  • - The language of mathematics, introduction to logic.
    - Definition of functions and basic properties of functions, elementary functions, domain of a function, determination of the basic properties of functions.
    - Graphs of functions.
    - Limit and continuity of functions, limit of a sequence.
    - Differential calculus of functions of one variable, derivatives, higher order derivatives, differential. Applications of derivatives, l'Hospital rule, geometrical meaning of the derivative at a point. Graphing functions.
    - Indefinite integral, methods of calculating indefinite integrals, integration by substitution, integration by parts, integration of rational functions, integration of irrational functions, integration of trigonometric functions, trigonometric substitution.
    - Definite integral, geometric applications of definite integrals, content figure, volume of a rotational body, an arc length of a plane curve, the content surfaces of revolution.
Literature
    recommended literature
  • Brožková, A. Cvičení z matematické analýzy II. pe. info
  • Cienciala, L., Ciencialová, L. Teorie grafů a grafové algoritmy. Slezská univerzita v Opavě, 2014. ISBN 978-80-7510-060-3. info
  • Došlá, Z., Kuben, J. Diferenciální počet funkcí jedné proměnné. Brno: MU, 2004. info
  • Míka, S., Drábek, P. Matematická analýza I. ZČU Plzeň, 2003. info
  • B. P. Děmidovič. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův brod, 2003. info
  • DEVLIN, K. Jazyk matematiky. Praha: Argo, 2002. ISBN 80-7203-470-7. info
  • Švejdar, V. Logika: neúplnost, složitost a nutnost. Praha, Academia, 2002. info
  • Sochor, A. Klasická matematická logika. Praha, Univerzita Karlova, 2001. info
  • Štěpánek, P. Matematická logika. Prraha, Univerzita Karlova, 2000. info
  • Jirků, P., Vejnarová, V. Neformální výklad základů formální logiky. VŠE Praha, 2000. URL info
  • Lukasová, A.:. Logické základy umělé inteligence I. Ostrava, 1999. info
  • Černý, I., Rokyta, M. Differential and integral calculus of one real variable. Praha, Karolinum, 1998. info
  • Brožková, A. Cvičení z matematické analýzy I. Pedagogická fakulta Ostravské univerzity, 1995. info
  • Jarník V. Diferenciální počet. Academia Praha, 1975. info
Teaching methods
Interactive lecture
Lecture with a video analysis
Assessment methods
Exam
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Credit: full-time students wrote the exercises two credit tests scoring 30 points each. All five students solve homework. For each homework gets 8 points. To obtain the credit needed 50 points. Points earned during the semester is multiplied by 0.4 and rounded up. Normalized points are counted for the exam.
Exam: Students may receive a maximum of 60 points from the exam. The successful it is necessary to obtain 30 points. To determine the mark of the test points earned in a semester of credit tests and the exam added. Maximum points is 100
The course is also listed under the following terms Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020.
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