Mathematical Analysis I

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Course Unit Code470-8721/01
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, English
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.
Summary
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; 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.
Recommended or Required Reading
Required Reading:
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: Matematická analýza 1, skripta VŠB-TUO.
J. Bouchala: Matematická analýza ve Vesmíru, http://www.am.vsb.cz/bouchala
Recommended Reading:
J. Stewart: Calculus, Belmont, California, Brooks/Cole Pub. Comp. 1987.
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
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Exercises evaluation and ExaminationCredit and Examination100 (100)51
        Exercises evaluationCredit30 10
        ExaminationExamination70 21