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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
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

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

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

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.

Aim of the course -

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

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: JARNIK/PEDF.CUNI.CZ (01.04.2009)

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

Teaching methods -

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

Lecture and seminar

Requirements to the exam -

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

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

Syllabus -

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

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.