# 470-2110/04 – Mathematical Analysis 1 (MA1)

 Gurantor department Department of Applied Mathematics Credits 5 Subject guarantor prof. RNDr. Jiří Bouchala, Ph.D. Subject version guarantor prof. RNDr. Jiří Bouchala, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties FEI Intended for study types Bachelor
Instruction secured by
KOV74 Mgr. Tereza Kovářová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2

### Subject aims expressed by acquired skills and competences

Students will get basic practical skills for work with fundamental concepts, methods and applications of differential and integral calculus of one-variable real functions.

Lectures
Tutorials
Project work

### Summary

In the first part of this subject, there are fundamental properties of the set of real numbers mentioned. Further, basic properties of elementary functions are recalled. Then limit of sequence, limit of function, and continuity of function are defined and their basic properties are studied. Differential and integral calculus of one-variable real functions is essence of this course.

### Compulsory literature:

J. Bouchala, M. Sadowská: Mathematical Analysis I (www.am.vsb.cz/bouchala)

### Recommended literature:

L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973

### Way of continuous check of knowledge in the course of semester

Tests, individual work.

### Other requirements

No additional requirements are imposed on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Real Number System. Real Functions of a Single Real Variable. Elementary Functions. Sequences of Real Numbers. Limit and Continuity of a Function. Differential and Derivative of a Function. Basic Theorems of Differential Calculus. Function Behaviour. Approximation of a Function by a Polynomial. Antiderivative (Indefinite Integral). Riemann’s (Definite) Integral.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 30  10
Examination Examination 70  21
Mandatory attendence parzicipation: Participation at all exercises is obligatory, 2 apologies are accepted. Participation at all lectures is expected.

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B0613A140010) Computer Science TZI P English Ostrava 1 Compulsory study plan
2019/2020 (B0613A140010) Computer Science TZI P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner