# 470-8721/01 – Mathematical Analysis I (MAINT)

 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 2010/2011 Year of cancellation Intended for the faculties FMT, FS, FEI, USP, HGF Intended for study types Bachelor
Instruction secured by
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3

### 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

### 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:

L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973. M. Demlová, J. Hamhalter: Calculus I, skripta ČVUT Praha 1996. J. Bouchala, M. Sadowská: Mathematical Analysis I (www.am.vsb.cz/bouchala)

### Recommended literature:

J. Stewart: Calculus, Belmont, California, Brooks/Cole Pub. Comp. 1987.

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

Průběžná kontrola studia: Studenti v průběhu semestru budou psát písemné testy. Za testy lze získat maximálně 30 bodů. Podmínky udělení zápočtu: K získání zápočtu je nutné získat minimálně 10 bodů.

### Other requirements

Additional requirements for students are not.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Real Number System; the Supremum Theorem. 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: 2012/2013 Winter semester)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 30  10
Examination Examination 70  21 3
Mandatory attendence participation: Attendance at discussions is obligatory (70 %). Attendance at lectures is expected.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3942) Nanotechnology (3942R001) Nanotechnology P English Ostrava 1 Compulsory study plan
2019/2020 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3968) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3942) Nanotechnology (3942R001) Nanotechnology P English Ostrava 1 Compulsory study plan
2018/2019 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2018/2019 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 1 Compulsory study plan
2017/2018 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2016/2017 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 1 Compulsory study plan
2016/2017 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 1 Compulsory study plan
2015/2016 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3942) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 1 Compulsory study plan
2014/2015 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3942) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2013/2014 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3942) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2012/2013 (B3942) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2011/2012 (B3942) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2010/2011 (B3942) Nanotechnology P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner