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Sequences and series - OENMM1706Z
Title: Sequences and series
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2020
Semester: both
E-Credits: 6
Hours per week, examination: 2/0, C+Ex [HT]
Capacity: winter:unknown / unknown (999)
summer:unknown / unknown (999)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Explanation: Rok3
Old code: POŘA
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
you can enroll for the course in winter and in summer semester
Guarantor: RNDr. František Mošna, Ph.D.
prof. RNDr. Ladislav Kvasz, DSc., Dr.
Class: Předměty v angličtině - mgr.
Classification: Mathematics > Real and Complex Analysis
Annotation -
Last update: Kateřina Esserová, DiS. (24.09.2019)
Number sequences (revision). Number series. Series with nonnegative terms, criteria of convergence. Alternating series, Leibniz criterion. Absolute and nonabsolute convergence, rearrangement of series. Sequences and series of functions, pointwise and uniform convergence. Power series, Taylor and Maclaurin series.
Aim of the course -
Last update: Kateřina Esserová, DiS. (24.09.2019)

To get the students acquainted with fundaments of the theory of sequences and series, to teach them investigate convergence in concrete cases. To emphasize the relation of pointwise and uniform convergence. To teach the students to work with power series.

Literature -
Last update: Kateřina Esserová, DiS. (24.09.2019)
  • Knopp, Konrad: Theory and Application of Infinite Series, Blackie London 1957
  • Hyslop, James M.: Infinite Series, Oliver and Boyd Edinburgh 1965
  • Singal, M. K., Singal, A. R.: A first cours in Real Analysis, R.Chand New Delhi 1999
  • Ross, K.A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer New York-Heidelberg-Berlin 1980
  • Fischer, E.: Intermediate Real Analisis. Undergraduate Texts in Mathematics, Springer NewYork-Heidelberg-Berlin 1983
  • Veselý, Jiří: Matematická analýza pro učitele, I, II, Matfyzpress Praha 1998
  • Kalas, Josef, Ráb, Miloš: Obyčejné diferenciální rovnice, MU Brno 2001
  • Plch, Roman: Příklady z matematické analýzy, Diferenciální rovnice, MU Brno 2002
  • Barták, Jaroslav: Diferenciální rovnice, Praha 1984
  • Došlá, Zuzana, Novák, Vítězslav: Nekonečné řady, MU Brno 2002
  • Pelikán, Štěpán, Zdráhal, Tomáš: Matematická analýza, Číselné řady,posloupnosti a řady funkcí, UJEP Ústí n. L. 1994
Teaching methods -
Last update: Kateřina Esserová, DiS. (24.09.2019)

Lecture and seminar
Requirements to the exam -
Last update: Kateřina Esserová, DiS. (24.09.2019)

- Credit requirements: active participation at seminars, succesful completion of the control tests (during the exam period there will be stated two terms for possible correction tests)
- Exam requirements: knowledge of given definitions, understanding of definitions, connections, relations, ability to solve problems
Syllabus -
Last update: Kateřina Esserová, DiS. (24.09.2019)

Sequnces: properties (sequences bounded, increasin, decreasing), cauchy sequences, subsequence, limits, Cauchy condition, limit points.
Series: introduction, properties, sum of series, convergence, tests (comparison, ratio, root, integral, Leibniz, Dirichlet, Abel, condensation), absolute and non-absolute convergence, rearrangement of series.
Sequencies and series of functions: pointwise and uniform convergence (Weierstrass test), statements on limits, continuity, derivatives and integrals, power series, properties, Taylor, Maclaurin series, expansion of basic elementary functions.
 
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