470-8721/02 – 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 languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesUSP, FMT, FS, HGFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
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.

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.

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

Written and oral exam.

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: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
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
2021/2022 (B0588A170002) Applied Sciences and Technologies MAT P English Ostrava 1 Compulsory study plan
2021/2022 (B0719A270002) Nanotechnology P English Ostrava 1 Compulsory study plan
2020/2021 (B0719A270002) Nanotechnology P English Ostrava 1 Compulsory study plan
2020/2021 (B0588A170002) Applied Sciences and Technologies MAT P English Ostrava 1 Compulsory study plan
2019/2020 (B0588A170002) Applied Sciences and Technologies MAT P English Ostrava 1 Compulsory study plan
2019/2020 (B0719A270002) Nanotechnology P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner