714-0067/01 – Bachelor Mathematics II (BMII)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorRNDr. Lubomír Pavelka, Ph.D.Subject version guarantorRNDr. Lubomír Pavelka, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2002/2003Year of cancellation2008/2009
Intended for the facultiesFBIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
H1O40 Mgr. Iveta Cholevová, Ph.D.
DRO03 Mgr. Jaroslav Drobek, Ph.D.
KRA44 Mgr. Kateřina Kozlová, Ph.D.
PAV20 RNDr. Lubomír Pavelka, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
ZID76 Mgr. Arnošt Žídek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

This course is closed. Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field matematics.

Teaching methods

Lectures
Individual consultations
Other activities

Summary

Integral calculus of function of one real variable: the indefinite integral, methods of evaluating integral, the definite integrals and applications, improper integral. Ordinary differential equations: separable equations, homogeneous equations, Bernoulli’s equation, linear equation of the first order, linear differential equations with constant coefficients. Infinite series of numbers, functional series, power series.

Compulsory literature:

[1] Kreml,P.: Mathematics II, VŠB-TU Ostrava 2005, ISBN 80-248-0798-X

Recommended literature:

[1] Vrbenská,H., Bělohlávková,J.: Základy matematiky pro bakaláře II. Skriptum VŠB-TUO, 1999. ISBN 80-7078-545-4

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Neurčitý integrál Primitivní funkce a neurčitý integrál funkce jedné reálné proměnné, základní integrační metody - substituce, per partes, integrace racionálních lomených funkcí, goniometrických funkcí, iracionálních funkcí. Určitý integrál Základní pojmy, vlastnosti, Newtonovo-Leibnizovo pravidlo, metody substituce a per partes v určitém integrálu, použití v geometrii (určení obsahu rovinné oblasti, délky oblouku křivky, objemu a povrchu rotačního tělesa) a ve fyzice. Diferenciální počet funkcí dvou proměnných Definice funkce dvou proměnných, definiční obor, limita a spojitost. Parciální derivace prvního řádu a vyšších řádů. Totální diferenciál. Rovnice tečné roviny a normály plochy. Extrémy funkcí dvou proměnných. Implicitně zadaná funkce a její derivace. Diferenciální rovnice obyčejné Diferenciální rovnice 1. řádu, druhy řešení. Separovatelné, homogenní a lineární rovnice. Lineární diferenciální rovnice 2. řádu s konstantními koeficienty, její řešení metodou variace konstant a metodou neurčitých koeficientů. Soustavy lineárních diferenciálních rovnic s konstantními koeficienty.

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 (100) 51
        Exercises evaluation Credit 20 (20) 0
                Written exam Written test 15  0
                Other task type Other task type 5  0
        Examination Examination 80 (80) 0
                Written examination Written examination 60  0
                Oral Oral examination 20  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2004/2005 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2003/2004 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner