# 470-2110/05 – Mathematical Analysis 1 (MA1)

 Gurantor department Department of Applied Mathematics Credits 6 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 Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FS, FEI Intended for study types Bachelor
Instruction secured by
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
DOR0059 Bc. Vojtěch Dorňák
KAB002 Ing. Pavla Hrušková, Ph.D.
JAH02 RNDr. Pavel Jahoda, Ph.D.
KOV74 Mgr. Tereza Kovářová, Ph.D.
KRA04 Mgr. Bohumil Krajc, Ph.D.
KRP0017 Ing. Daniel Krpelík
KRU0097 Bc. Jakub Kružík
KUB59 RNDr. Michael Kubesa, Ph.D.
VOD03 doc. Mgr. Petr Vodstrčil, Ph.D.
S1A64 RNDr. Petra Vondráková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Part-time Credit and Examination 12+12

### 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. Written exam.

### 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

Part-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: *

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### Occurrence in special blocks

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