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 | 2 | 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 |
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:
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.