FPF:UIMOIBK004 Mathematics I - Course Information

UIMOIBK004 Mathematics I

Extent and Intensity

0/0/0. 6 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

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

• Information and communication technologies (programme FPF, MOI)

Course objectives

The aim of the course is to acquaint students with the basic concepts of mathematical analysis.

Syllabus

• 1. The language of mathematics, an introduction to logic.
• 2. Concept of function, basic properties of function, elementary functions, definitional domain of function, determination of basic properties of a function.
• 3.-4. Graph of a function.
• 5.-6. Limit and continuity of a function, limit of a sequence.
• 7.-8. Differential calculus of a function of one real variable, derivatives, higher order derivatives, differential of a function. Application of derivative, l ́Hospital's rule, geometric meaning of derivative of a function at a point.
• 9. The progression of a function.
• 10.-11. Indefinite integral, methods of calculating the indefinite integral, integration by substitution, integration per partes method, integration of rational function, integration of irrational function, integration of goniometric functions, goniometric substitution.
• 12.-13. Definite integral, geometric application of definite integral, content of a figure, volume of a rotating solid, length arc length of a plane curve, content of a rotating surface.

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
Information on the extent and intensity of the course: 14 hod/sem.

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

• Enrolment Statistics (Winter 2023, recent)
  
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