SubjectsSubjects(version: 837)
Course, academic year 2018/2019
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Mathematics 1 - NMMA711
Title in English: Matematika 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 7
Hours per week, examination: winter s.:4/4 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Additional information: http://www.karlin.mff.cuni.cz/~barta/
Guarantor: doc. RNDr. Miroslav Zelený, Ph.D.
Classification: Mathematics > Real and Complex Analysis
Interchangeability : JEB118
Is pre-requisite for: NMMA712
In complex pre-requisite: JEB104
Annotation -
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.
Course completion requirements
Last update: doc. RNDr. Pavel Pyrih, CSc. (27.11.2018)

midterm test: 30 points

homeworks: 20 points

final exam: 50 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"

Midterm is a 70 minutes test which takes part approximately in the half of the semester. The exam is about real numbers and sequences. There are two attempts, where the better result is taken into account.

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. Lecture notes and

other materials are allowed, electronic devices are prohibited.

Oral part follows typically the day after the written exam. The oral part

tests understanding the definitions and theorems and 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 - Czech
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 -
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.

 
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