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Mathematical Analysis 1

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-2110/05
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
BOU10prof. RNDr. Jiří Bouchala, Ph.D.
S1A64RNDr. Petra Vondráková, Ph.D.
JAH02RNDr. Pavel Jahoda, Ph.D.
VOD03doc. Mgr. Petr Vodstrčil, Ph.D.
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
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
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
Required Reading:
J. Bouchala, M. Sadowská: Mathematical Analysis I (
J. Bouchala: Matematická analýza 1, skripta VŠB-TUO.
J. Bouchala: Matematická analýza ve Vesmíru,
P. Šarmanová, J. Kuben, Š. Hošková, P. Račková: Diferenciální a integrální počet funkcí jedné proměnné,
J. Bouchala, M. Sadowská: Mathematical Analysis I (
Recommended Reading:
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973
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
Planned learning activities and teaching methods
Lectures, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 10
        ExaminationExamination70 21