UIINK05 Mathematical Analysis I

Faculty of Philosophy and Science in Opava
Winter 2023
Extent and Intensity
16/0/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michaela Mlíchová, Ph.D. (lecturer)
RNDr. Šárka Vavrečková, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Michal Málek, Ph.D.
Mathematical Institute in Opava
Timetable
Fri 13. 10. 8:05–9:35 R1, Fri 24. 11. 11:15–12:45 R1, Fri 8. 12. 9:30–11:00 R2
Course Enrolment Limitations
The course is offered to students of any study field.
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. ISBN 80-7200-587-1. 2003. info
  • REKTORYS, K. Přehled užité matematiky 1. Praha : Prometheus. ISBN 80-7196-180-9. 2000. info
  • REKTORYS, K. a spol. Přehled užité matematiky 2. Praha : Prometheus. ISBN 80-7196-181-7. 2000. 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 (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Information on the extent and intensity of the course: Přednáška 16 HOD/SEM.
The course is also listed under the following terms Winter 2019, Winter 2020, Winter 2021, Winter 2022.
  • Enrolment Statistics (recent)
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