Sequences and series - ORMA10109
Title: Číselné posloupnosti a řady
Form of teaching: lecture+practicals
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2013
Duration in semesters: 1
Semester: summer
E-Credits: 4
Examination process: summer s.:
Hours per week, examination: summer s.:0/0, C+Ex [HS]
Extent per academic year: 16 [hours]
Capacity: unknown / unknown (999)
Maximum number of enrolled students: 999
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Repeated enrollment: 2 / 2 / 3 / 2
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
Guarantor: doc. RNDr. Jiří Jarník, CSc.
Mgr. Derek Pilous, Ph.D.
prof. RNDr. Ladislav Kvasz, DSc., Dr.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
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Annotation -
The one term course is focused on the basic notions of mathematical analysis: the limit of an infinite sequence and the convergence of an infinite series. The historical context and the connections with other branches of mathematics will be considered. The students will be presented the basic methods of proofs as well as the typical patterns of argumentation, which they will use in other branches of mathematical analysis.
Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)
Aim of the course -

The aim of the subject is the introduction of the basic notions of mathematical analysis (the limit of a sequence, convergence of a infinite series) together with study of the historical connections and search for connections to other mathematical disciplines and use in computers and appropriate mathematical software.

Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)
Literature -

§ Jarník, V.: Diferenciální počet I, II. Praha: Academia 1984.

§ Jarník, J.: Posloupnosti a řady. Praha: Mladá fronta, 1979.

§ Kubínová, M. - Novotná, J.: Posloupnosti a řady. Matematická analýza, teoretická aritmetika. [Skriptum.] Praha: Karolinum 1997.

§ Novotná, J. a kol.: Sbírka úloh z matematiky (nejen) pro přípravu k maturitě a přijímacím zkouškám na vysoké školy. Praha, Scientia 1997.

§ Veselý, J.: Matematická analýza pro učitele, I. a II. díl, Praha: MATFYZPRESS, 2004.

§ Snítal, J. - Šalát, T.: Posloupnosti a řady pro 3. ročník gymnázií se zaměřením na matematiku. Praha, SPN 1986.

§ Děmidovič, B.P.: Sbírka úloh a cvičení z matematické analýzy. Fragment, Praha 2004

Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)
Teaching methods -

lecture and exercises

Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)
Syllabus -
arithmetical progression,

limit of a sequence,

operations with limits of sequences,

infinite series, the sum of an infinite series,

criteria of convergence of series with nonnegative members,

alternating series,

absolute and non absolute convergence,

generalized associative and commutative law.

Last update: JANCARIK/PEDF.CUNI.CZ (09.06.2010)