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

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFS, FEI, HGF, USP, FMTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
SAD015 Ing. Marie Sadowská, 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.

Teaching methods

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.

E-learning

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)
Task nameType of taskMax. number of points
(act. for subtasks)
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

Assessment of instruction



2022/2023 Winter
2021/2022 Winter
2020/2021 Winter
2019/2020 Winter
2018/2019 Winter
2017/2018 Winter
2016/2017 Winter
2015/2016 Winter
2013/2014 Winter
2012/2013 Winter