Mathematics 1 - NMMA711

• Title: Matematika 1
• Guaranteed by: Department of Mathematical Analysis (32-KMA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2021
• Semester: winter
• E-Credits: 7
• Hours per week, examination: winter s.:4/4, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Additional information: http://www.karlin.mff.cuni.cz/~barta/
• Classification: Mathematics > Real and Complex Analysis
• Interchangeability : JEB118
• Is incompatible with: JEB118
• Is pre-requisite for: NMMA712
• Is interchangeable with: JEB118

Annotation

English

Last update: doc. Mgr. Petr Kaplický, Ph.D. (14.09.2017)

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: G_M (07.05.2014)

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: doc. Mgr. Petr Honzík, Ph.D. (24.09.2019)

To be eligible to take the exam, the students must actively participate in the course.

Towards the end of the semester, there will be a practise written exam, where a few bonus points for the final exam may be gained.

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"

Final Exam takes part in the examination period at the end of the semester

and consists of two parts.

Written part. Students have 90 minutes to solve problems on limit of a

function, derivatives, investigation of a function. The students may NOT use any literature or electronic devices

during the test.

Oral part follows typically the day after the written exam. 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: doc. RNDr. Miroslav Zelený, Ph.D. (11.05.2018)

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

Syllabus

English

Last update: doc. RNDr. Tomáš Bárta, Ph.D. (12.09.2017)

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.

Czech

Last update: doc. RNDr. Tomáš Bárta, Ph.D. (12.09.2017)

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.