# 714-0067/02 – Bachelor Mathematics II (BMII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor RNDr. Lubomír Pavelka, Ph.D. Subject version guarantor Fiktivní Uživatel Study level undergraduate or graduate Requirement Compulsory Year Semester summer Study language Czech Year of introduction 1999/2000 Year of cancellation 2009/2010 Intended for the faculties FBI Intended for study types Bachelor
Instruction secured by
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
PAV20 RNDr. Lubomír Pavelka, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 18+0

### 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

### 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). 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 neurčitých koeficientů. Soustavy lineárních diferenciálních rovnic s konstantními koeficienty.

### Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20 (20) 0
Examination Examination 80 (80) 0
Written examination Written examination 60  0
Oral Oral examination 20  0
Mandatory attendence parzicipation:

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### 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 K Czech Praha Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Ostrava Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Most Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Praha 1 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Ostrava 1 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Most 1 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Praha 1 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Ostrava 1 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Most 1 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Praha 1 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Ostrava 1 Compulsory study plan
2004/2005 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Ostrava 1 Compulsory study plan
2003/2004 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 1 Compulsory study plan
2003/2004 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI K Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner