Course Unit Code | 470-8721/01 |
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Number of ECTS Credits Allocated | 6 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. |
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; the Supremum Theorem.
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.
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Recommended or Required Reading |
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Required Reading: |
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L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.
M. Demlová, J. Hamhalter: Calculus I, skripta ČVUT Praha 1996.
J. Bouchala, M. Sadowská: Mathematical Analysis I (www.am.vsb.cz/bouchala) |
J. Bouchala: Matematická analýza 1, skripta VŠB-TUO.
J. Bouchala: Matematická analýza ve Vesmíru, http://www.am.vsb.cz/bouchala |
Recommended Reading: |
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J. Stewart: Calculus, Belmont, California, Brooks/Cole Pub. Comp. 1987.
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P. Šarmanová a kol.: Diferenciální (a integrální) počet funkcí jedné proměnné, http://www.am.vsb.cz/sarmanova/cd/index.htm
J. Brabec, F. Martan, Z. Rozenský: Matematická analýza I. Praha, SNTL 1985.
B. Budinský a J. Charvát: Matematika I. Praha, SNTL 1987.
K. Rektorys a kol.: Přehled užité matematiky I a II. Praha, Prometheus 1995.
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973 (anglicky).
M. Demlová, J. Hamhalter: Calculus I, skripta ČVUT Praha 1996 (anglicky).
J. Stewart: Calculus, Belmont, California, Brooks/Cole Pub. Comp. 1987 (anglicky). |
Planned learning activities and teaching methods |
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Lectures, Tutorials |
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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Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
Exercises evaluation | Credit | 30 | 10 |
Examination | Examination | 70 | 21 |