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Course, academic year 2022/2023
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Mathematics I - JEB118
Title: Mathematics I
Guaranteed by: Institute of Economic Studies (23-IES)
Faculty: Faculty of Social Sciences
Actual: from 2021 to 2022
Semester: winter
E-Credits: 7
Examination process: winter s.:
Hours per week, examination: winter s.:4/4, C+Ex [HT]
Capacity: 27 / 27 (25)
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: RNDr. Kristýna Kuncová, Ph.D.
Teacher(s): Oleksandr Minakov, Ph.D.
Buddhika Priyasad Sembukutti Liyanage, Ph.D.
Class: Courses not for incoming students
Incompatibility : NMMA711
Interchangeability : NMMA711
Is incompatible with: JEB139
Is pre-requisite for: JEB119
Is interchangeable with: NMMA711
In complex pre-requisite: JEB104
Last update: ZELENY (14.02.2012)
Basic definitions and theorems from the theory of real functions of one variable
will be presented.

Aim of the course -
Last update: Ing. Pavel Kot (15.04.2021)

A basic course of mathematics for students of FSV UK - the first semester. Students become familiar with

mathematical analysis of functions of one variable. The presented methods are

convenient for solving problems in economy.

Course completion requirements
Last update: RNDr. Kristýna Kuncová, Ph.D. (27.09.2023)

During the semester there will be homeworks (30 points), midterm (15 points) and final exam during the exam period (55 points).

Grading: The total score is obtained as the sum of the points. The final
grade depends on the total score as follows.

51-60 points ... "E"
61-70 points ... "D"
71-80 points ... "C"
81-90 points ... "B"
91-100 points ... "A"

The midterm exam consists of two limits of a sequence.

Final Exam takes part in the examination period at the end of the semester
and consists of two parts.

Written part. Students have 120 minutes to solve problems on limits of a function, investigation of a function. The students may use any literature, but no electronic devices
during the test.

The oral part tests understanding the definitions and theorems and selected proofs and the ability to apply
them. During the oral part only pencil and paper are allowed. Each student
should prepare answers within approximately 40 minutes. Then the student
should present answers and should answer complementary questions.

Last update: Ing. Pavel Kot (15.04.2021)

Hájkova, Johanis, John, Kalenda, Zelený: Mathematics

Further reading:

A,. C. Chiang: Fundamental Methods of Mathematical Economics, McGraw-Hill Education

V. A. Zorich: Mathematical analysis I, Springer, 2004

W. Rudin: Principles of mathematical analysis, McGraw-Hil, Inc., 1976

Teaching methods
Last update: ZELENY (14.02.2012)

Lectures and seminars.

Requirements to the exam
Last update: ZELENY (14.02.2012)

Written and oral exam.

Syllabus -
Last update: ZELENY (14.02.2012)

Real numbers, supremum and infimum, minimum and maximum.

Limit of a sequence and its basic properties, arithmetics of limits, limit of a monotone sequence, Weierstrass theorem.

Functions of one real variable: limit of a function, elementary functions and their properties,
derivative, properties of continuous functions, Langrange mean value theorem, extrema and their finding,
convexity, examination and construction of graphs of functions.

Entry requirements
Last update: Ing. Pavel Kot (15.04.2021)

1. Introduction: sets, logic, sets of numbers, supremum and infimum, minimum and maximum.

2. Sequences: limit of a sequence - finite and infinite, theorem on limit of a monotone sequence.

3. Functions of one variable: limit of function, elementary functions and their properties, derivative, properties of continuous functions, Langrange theorem, finding of extrema, convex and concave functions, investigation of function and construction of its graph.

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