| Course Unit Code | 470-2110/01 |
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| Number of ECTS Credits Allocated | 8 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| BOU10 | prof. RNDr. Jiří Bouchala, Ph.D. |
| SAD015 | Ing. Marie Sadowská, Ph.D. |
| Summary |
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| In the first part of this subject, there are fundamental properties of the set of real numbers mentioned. Further, basic properties of elementary functions are recalled. Then limit of sequence, limit of function, and continuity of function are defined and their basic properties are studied. Differential and integral calculus of one-variable real functions is essence of this course. |
| Learning Outcomes of the Course Unit |
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| Students will get basic practical skills for work with fundamental concepts, methods and applications of differential and integral calculus of one-variable real functions. |
| Course Contents |
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Real Number System.
Real Functions of a Single Real Variable.
Elementary Functions.
Sequences of Real Numbers.
Limit and Continuity of a Function.
Differential and Derivative of a Function.
Basic Theorems of Differential Calculus.
Function Behaviour.
Approximation of a Function by a Polynomial.
Antiderivative (Indefinite Integral).
Riemann’s (Definite) Integral. |
| Recommended or Required Reading |
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| Required Reading: |
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| BOUCHALA, Jiří; SADOWSKÁ, Marie. Mathematical Analysis I, 2007. http://www.am.vsb.cz/bouchala |
BOUCHALA, Jiří. Matematická analýza 1. 2. vyd. Ostrava: VŠB - Technická univerzita Ostrava, 2005. ISBN 80-248-0933-8.
BOUCHALA, Jiří. Matematická analýza I: transparenty. Ostrava: VŠB - Technická univerzita Ostrava, 2007. ISBN 978-80-248-1374-5.
BOUCHALA, Jiří. Matematická analýza ve Vesmíru,
http://www.am.vsb.cz/bouchala
BOUCHALA, Jiří; SADOWSKÁ, Marie. Mathematical Analysis I, 2007.
http://www.am.vsb.cz/bouchala |
| Recommended Reading: |
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| ANTON, Howard; BIVENS, Irl a DAVIS, Stephen. Calculus. 8th ed. Hoboken: Wiley, c2005. ISBN 0-471-48273-0. |
VESELÝ, Jiří. Základy matematické analýzy. První díl. Vydání druhé. Odborná edice MatfyzPress. Praha: Matfyzpress, 2019. ISBN 978-80-7378-389-1.
VESELÝ, Jiří. Základy matematické analýzy. Druhý díl. Praha: Matfyzpress, 2009. ISBN 978-80-7378-063-0.
ANTON, Howard; BIVENS, Irl a DAVIS, Stephen. Calculus. 8th ed. Hoboken: Wiley, c2005. ISBN 0-471-48273-0. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 | 10 |
| Examination | Examination | 70 | 21 |