SubjectsSubjects(version: 964)
Course, academic year 2024/2025
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Sequences and series - O02310006
Title: Posloupnosti a řady
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2022
Semester: winter
E-Credits: 4
Examination process: winter s.:
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
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
Guarantor: prof. RNDr. Ladislav Kvasz, DSc., Dr.
Classification: Mathematics > Real and Complex Analysis
Is pre-requisite for: OSOZ1M, O0231SOUB
Annotation -
Number sequences (revision). Number series. Series with nonnegative terms, criteria of convergence. Alternating series, Leibniz criterion. Absolute and nonabsolute convergence. Associative and commutative law for infinite series. Sequences and series of functions, pointwise and uniform convergence. Power series, Taylor and Maclaurin series.
Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Aim of the course -

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.

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Literature -

Fischer, E.: Intermediate Real Analysis, Springer Verlag, New York-Heidelberg-Berlin 1984

Ross, K.A.: Elementary Analysis: The Theory of Calculus, Springer Verlag, New York-Heidelberg-Berlin 1980

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Teaching methods -

Lecture and seminar

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Requirements to the exam -

Seminar:

  • regular active attendance
  • correct elaboration of homeworks
  • passing current tests

Exam:

  • Knowledge of definitions, theorems and proofs and ability to illustrate them by examples and counterexamples
  • ability of solving problems with help of the theoretical knowledge
Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Syllabus -

Sequences (review): definition, properties; limit of a sequence.

Series: sum of a series. Series with nonnegative terms, criteria of convergence. Alternating series, Leibniz criterion. Absolute and nonabsolute convergence.

Sequences and series of functions. Pointwise and uniform convergence. Associative and commutative law for infinite series. Interchanging operations.

Power series. Taylor and Maclaurin series for elementary functions.

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
 
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