FPF:UIIABP0004 Mathematics I - Course Information
UIIABP0004 Mathematics I
Faculty of Philosophy and Science in OpavaWinter 2023
- Extent and Intensity
- 2/3/0. 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 - Timetable
- Mon 8:05–9:40 B1
- Timetable of Seminar Groups:
- 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
- Computer science and English (programme FPF, In-An-bp)
- Course objectives
- The aim of the course is to acquaint students with the basic concepts of mathematical analysis.
- 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. 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
- 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)
- Permalink: https://is.slu.cz/course/fpf/winter2023/UIIABP0004