UIINP05 Mathematical Analysis I

Faculty of Philosophy and Science in Opava
Winter 2024
Extent and Intensity
3/4/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Málek, Ph.D. (lecturer)
Mgr. Veronika Rýžová (seminar tutor)
Mgr. Michaela Záškolná (seminar tutor)
RNDr. Šárka Vavrečková, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Michal Málek, Ph.D.
Mathematical Institute in Opava
Timetable
Wed 9:45–12:10 R1
  • Timetable of Seminar Groups:
UIINP05/A: Tue 15:35–17:10 R1, Thu 16:25–18:00 R2, M. Záškolná
UIINP05/B: Mon 8:05–9:40 R1, Thu 14:45–16:20 R2, V. Rýžová
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 course Mathematical analysis I deals mainly with differential calculus of functions of one real variable. The basic concepts studied in this course include limit, continuity and derivative.
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. Fundamentials (statements and operations with statements, sets and systems of sets, operations with sets, cartesian product of sets, binary relations, mappings)
  • 2. Real numbers (axiomatic definition, continuity axiom, set of natural numbers, principle of mathematical induction, integers, rational numbers, irrational numbers, infimum, supremum,   infime theorem,   suprem theorem, extended set of real numbers, interval, neighborhood of point)
  • 3. The concept of a function (domain and range of function values, function graph, function boundary, evenness, oddity, periodicity, monotonicity of a function at a   point and on a set, composition of functions, inverse functions)
  • 4. Real sequences (sequence limit,   limit theorems, Euler number, selected sequence, mass sequence points, limes superior, limes inferior)
  • 5. Limit and continuity of a function (limit, theorems on   limits, continuity of a function at a   point, continuity of a function on an interval, points of discontinuity)
  • 6. Derivative of a function (derivative and its geometrical meaning, derivative theorems, derivative of elementary functions, mean value theorem, l'Hospital rule)
  • 7. Function (monotonicity, extremes, convexity, concavity, inflection points, asymptotes)
  • 8. Approximate expression of a function (differential, Taylor formula)
Literature
    required literature
  • • KUBEN, J., P. ŠARMANOVÁ. Diferenciální počet funkcí jedné proměnné. Ostrava: VŠB-TU, 2006.
  • Došlá, Z., Kuben, J. Diferenciální počet funkcí jedné proměnné. Brno: MU, 2004. info
    recommended literature
  • NOVÁK, V. Diferenciální počet v R. Praha: SPN, 1985.
  • Děmidovič Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 2003. ISBN 80-7200-587-1. info
  • REKTORYS, K. Přehled užité matematiky 1. Praha : Prometheus, 2000. ISBN 80-7196-180-9. info
  • REKTORYS, K. a spol. Přehled užité matematiky 2. Praha : Prometheus, 2000. ISBN 80-7196-181-7. info
  • L. Zajíček. Vybrané úlohy z matematické analýzy. Matfyzpress, Praha, 2000. info
  • A. P. Mattuck. Introduction to Analysis. Prentice Hall, New Jersey, 1999. info
  • K. Polák. Přehled středoškolské matematiky. SPN, 1991. info
  • R. A. Adams. Single Variable Calculus. Addison-Weseley Publischers Limited, 1983. info
  • L. Leithold. The Calculus with Analytic Geometry. Harper & Row, 1981. info
  • S. I. Grossmann. Calculus. Academic Press, 1977. info
  • V. Jarník. Diferenciální počet I. ČSAV, Praha, 1963. info
Teaching methods
Lectures, exercises
Assessment methods
Attendance at lectures is desirable; During the first lecture and the first exercise, students will be acquainted with the requirements of the lecturer. The exam consists of two parts - written and oral. Successful completion of the written part is followed by an oral part, where the knowledge of the subject matter is further tested.
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023.
  • Enrolment Statistics (recent)
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