Mathematics I - JEB118

• Title: Mathematics I
• Guaranteed by: Institute of Economic Studies (23-IES)
• Faculty: Faculty of Social Sciences
• Actual: from 2023
• Semester: winter
• E-Credits: 7
• Examination process: winter s.:
• Hours per week, examination: winter s.:4/4, Ex [HT]
• Capacity: 59 / 59 (unknown)
• Min. number of students: unlimited
• 4EU+: no
• 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): RNDr. Kristýna Kuncová, Ph.D.; Mgr. Michael Zelina
• 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

Annotation

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

English

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.

Czech

Last update: Ing. Pavel Kot (15.04.2021)

Základní přednáška z matematiky pro FSV UK - první semestr.

Studenti se seznámí zejména s matematickou analýzou funkcí jedné reálné proměnné. Přednášené metody jsou vhodné pro řešení ekonomických úloh.

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.

Literature

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

English

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.

Czech

Last update: Ing. Pavel Kot (15.04.2021)

1. Úvod: Množiny, logika, číselné množiny, supremum a infimum, nejmenší a největší prvek.

2. Posloupnosti: vlastní a nevlastní limita, věta o limitě monotónní posloupnosti.

3. Funkce jedné reálné proměnné: limita funkce, elementární funkce a jejich vlastnosti, derivace, vlastnosti spojitých funkcí, Langrangeova věta o střední hodnotě, extrémy a jejich vyšetřování, konvexita a konkávnost, vyšetření průběhu funkce.

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.