151-0449/02 – Sequences and Series (PaR)

Gurantor department	Department of Mathematical Methods in Economics	Credits	3
Subject guarantor	prof. RNDr. Dana Šalounová, Ph.D.	Subject version guarantor	RNDr. Alena Poloučková
Study level	undergraduate or graduate	Requirement	Choice-compulsory
Year	1	Semester	winter
		Study language	Czech
Year of introduction	2006/2007	Year of cancellation	2010/2011
Intended for the faculties	EKF	Intended for study types	Follow-up Master

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
POL95	RNDr. Alena Poloučková

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Part-time	Credit	0+6
Distance	Credit and Examination	0+6
Lifelong	Credit and Examination	0+3

Subject aims expressed by acquired skills and competences

Sequences and Series 1. Knowledge • summarize the basic knowledge of number sets theory • explain and characterize sequences of real numbers 2. Comprehension • clarify the term “limits of sequences” 3. Application • develop tools for approximate calculations of functional values 4. Analysis • classify some important functions with these series 5. Synthesis • arrange basic knowledge of functional number series • formulate relations between sequences and their limits 6. Evaluation • interpret basic problems related to infinite and functional series • explain various problems related to sequences

Teaching methods

Lectures
Individual consultations

Summary

This course aims to provide the basic definitions of terms from the theories of sequences, infinite number and functional series. It will thus develop and use knowledge from previous basic mathematical courses, because mathematical education cultivates one’s attitude to problem solving in various areas of the economy and it helps reveal their nature. Infinite progressions (numerical and functional) are among the most frequently used and most efficient methods of mathematical analysis and numeric calculation.

Compulsory literature:

Study materials created for this course are available through the Moodle system.

Recommended literature:

doporučené studijní materiály: COUFAL, J., KLŮFA, J., KAŇKA, M., HENZLER, J.: Učebnice matematiky pro ekonomické fakulty. Victoria Publishing, a.s. Praha,1996. ISBN 80-7187-148-6. OŠŤÁDALOVÁ, E., POLOUČKOVÁ, A.: Řady a jejich užití. VŠB – TU Ostrava, 2000.ISBN 80-7078-769-4. další doporučená literatura: BUDINSKÝ, B., CHARVÁT,J.: Matematika I. SNTL Praha 1987. ŠKRÁŠEK, J., TICHÝ, Z.: Základy aplikované matematiky II. SNTL Praha 1986. ŠALÁT, T.: Nekonečné řady. Praha, Academia 1974. VOROB´EV, N. N.: Teorija rjadov.3. izd. Moskva, Nauka 1976.

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Osnova předmětu: 1. Posloupnosti- pojem posloupnosti reálných čísel, konvergentní a divergentní posloupnosti. 2. Nekonečné číselné řady – základní pojmy, geometrická řada, některé věty o konvergentních řadách. 3. Kriteria konvergence a divergence pro řady s kladnými členy. 4. Alternující řady. Absolutně konvergentní řady. 5. Funkční řady, jejich obor konvergence. 6. Stejnoměrná konvergence, vlastnosti stejnoměrně konvergentních řad. 7. Mocninné řady. Stejnoměrní konvergence mocninných řad. 8. Taylorova a Maclaurinova řada.

Conditions for subject completion

Distance form (validity from: 2009/2010 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Exercises evaluation and Examination	Credit and Examination	100 (100)	51	3
Exercises evaluation	Credit	45 (45)	23	3
Written exam	Written test	45	23	3
Examination	Examination	55 (55)	28	3
Written examination	Written examination	55	28	3

Mandatory attendence participation:

Show history

Conditions for subject completion and attendance at the exercises within ISP:

Show history

Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Year	Type of duty
2010/2011	(N6207) Quantitative Methods in Management	(6207T018) Quantitative management support	D	Czech	Ostrava	2	Choice-compulsory	study plan
2009/2010	(N6207) Quantitative Methods in Management	(6207T018) Quantitative management support	D	Czech	Ostrava	1	Choice-compulsory	study plan
2009/2010	(N6207) Quantitative Methods in Management	(6207T018) Quantitative management support	D	Czech	Ostrava	2	Choice-compulsory	study plan
2008/2009	(N6207) Quantitative Methods in Management	(6207T018) Quantitative management support	D	Czech	Ostrava	1	Choice-compulsory	study plan
2008/2009	(N6207) Quantitative Methods in Management	(6207T018) Quantitative management support	D	Czech	Ostrava	2	Choice-compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

Předmět neobsahuje žádné hodnocení.