Course detail

Mathematic Analysis 1

FP-Vma1PAcad. year: 2013/2014

In the introductory course “Mathematical Analysis I”, students majoring in Mathematical Methods in Economics are familiarised with the fundamental concepts of differential and integral calculus of functions in one real variable. The acquired knowledge is a starting point not only for further study of Mathematical Analysis, but also a necessary assumption for study of economics and theoretical technical disciplines, as well as for practical solving of problems in these disciplines.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. RNDr. Miroslav Kureš, Ph.D.

Department

Institute of Informatics (ÚI)

Learning outcomes of the course unit

Calculus count methods for applications in economical disciplines.

Prerequisites

Knowledge of mathematics in secondary school level.

Co-requisites

Not applied.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course-unit credit is conditional on attendance. Examination: oral

Course curriculum

1. Functions. Basic concepts.
2. Polynomials. Roots of polynomials.
3. Sequences. Limits.
4. Limits of functions. The continuity.
5. Derivations. The L'Hospital rule.
6. Differentials. Higher order derivations and differentials. Taylor polynomials.
7. Stationary points and extremes.
8. Inflection points. Asymptotes.
9. Curves.
10. The indefinite integral.
11. Methods of integration.
12. The Riemann integral.
13. Applications of the Riemann integral.

Work placements

Not applicable.

Aims

Students will be made familiar with fundaments of differential and integral calculus in one real variable. They will be able to apply it in various engineering tasks.

Specification of controlled education, way of implementation and compensation for absences

Seminars: required
Lectures: recommended

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

V. Jarník: Diferenciální počet I, Academia, 1984 (CS)
V. Jarník: Integrální počet I, Academia, 1984 (CS)
E. A. Ok: Real Analysis with Economic Applications, Princeton University Press, 2007 (EN)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BAK-KME Bachelor's

    branch BAK-MME , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

doc. RNDr. Miroslav Kureš, Ph.D.

Syllabus

1. Functions. Basic concepts.
2. Polynomials. Roots of polynomials.
3. Sequences. Limits.
4. Limits of functions. The continuity.
5. Derivations. The L'Hospital rule.
6. Differentials. Higher order derivations and differentials. Taylor polynomials.
7. Stationary points and extremes.
8. Inflection points. Asymptotes.
9. Curves.
10. The indefinite integral.
11. Methods of integration.
12. The Riemann integral.
13. Applications of the Riemann integral.

Exercise

39 hours, compulsory

Teacher / Lecturer

doc. RNDr. Miroslav Kureš, Ph.D.