714-0401/01 – Mathematical Analysis I ()

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits8
Subject guarantorRNDr. Dagmar PíšováSubject version guarantorRNDr. Dagmar Píšová
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction1999/2000Year of cancellation2006/2007
Intended for the facultiesFEIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA44 Mgr. Kateřina Kozlová, 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

Teaching methods

Summary

The topic is oriented to the function of one real variable that are studied using infinitesimal calculus. Limits and continuity, derivatives and differentials are applied to the function properties analysis. Integral calculus (indefinite and definite integrals) is introduced from the point of view of gemtrical and physical applications.

Compulsory literature:

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Osnova předmětu Funkce a jejich vlastnosti Množina reálných čísel; funkce - vlastnosti, operace; elementární funkce; číselné posloupnosti; limita a spojitost funkce Diferenciální počet funkcí jedné proměnné Derivace funkce - zavedení, derivace operací, derivace elementárních funkcí; věta o přírůstku funkce, diferenciál; derivace a diferenciály vyšších řádů, Taylorův rozvoj; parametricky zadané funkce a jejich derivace, rovinné křivky; základní věty diferenciálního počtu; monotónnost funkce, extrémy; konvexnost, konkávnost, inflexní body; L'Hospitalovy věty, asymptoty; průběh funkce. Integrální počet funkcí jedné proměnné Neurčitý integrál: vlastnosti, metody integrace ("per partes", substituce), integrace racionálních funkcí. Určitý integrál: zavedení, vlastnosti, výpočet, geometrické aplikace; integrály s proměn-nou mezí, nevlastní integrály.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

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2005/2006 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 1 Compulsory study plan
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2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava 1 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava 1 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 1 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava 1 Compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner