714-0367/04 – Mathematics II (MII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor Ing. Petra Schreiberová, Ph.D. Subject version guarantor Mgr. Iveta Cholevová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 1999/2000 Year of cancellation 2019/2020 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
H1O40 Mgr. Iveta Cholevová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
KRC76 Mgr. Jiří Krček
LUN44 Mgr. Milena Luňáčková, Ph.D.
SKN002 Ing. Petra Schreiberová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 12+4

Subject aims expressed by acquired skills and competences

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 mathematics.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Integral calculus of function of one real variable: the indefinite and definite integrals, properties of the indefinite and definite integrals, application in the geometry and physics. Differential calculus of functions of several independent variables. Ordinary differential equations of the first and the second order.

Compulsory literature:

Kreml, P.: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X

Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

Way of continuous check of knowledge in the course of semester

zápočet za zpracování zadaného programu může student získat až 20 bodů zkouška Kombinovanou zkoušku tvoří praktická část (60 minut, příklady) a teoretická část (20 minut, teoretické otázky). Praktická část je hodnocena 0 - 60 body, teoretická část 0 - 20 body. Aby student u zkoušky uspěl musí získat v praktické části nejméně 25 bodů a v teoretické části nejméně 5 bodů. klasifikace získané body známka 86 - 100 výborně 66 - 85 velmi dobře 51 - 65 dobře 0 - 50 nevyhověl Soubor otázek k teoretické části zkoušky 1. Primitivní funkce a neurčitý integrál 2. Integrace neurčitého integrálu substitucí 3. Integrace neurčitého integrálu metodou per partes 4. Integrace funkce racionální lomené. 5. Integrace goniometrických funkcí 6. Integrace iracionálních funkcí, vyšší transcendentní funkce. 7. Pojem Riemannova určitého integrálu 8. Vlastnosti Riemannnových určitých integrálů 9. Substituce v určitém integrálu 10. Geometrické aplikace určitého integrálu 11. Určení obsahu rovinné plochy 12. Určení objemu rotačního tělesa 13. Určení délky křivky 14. Určení povrchu rotační plochy 15. Funkce více proměnných – definice, definiční obor, graf 16. Parciální derivace funkce více proměnných 17. Totální diferenciál funkce více proměnných 18. Rovnice tečné roviny a normály k ploše 19. Extrémy funkce více proměnných 20. Obyčejné diferenciální rovnice 21. Typy řešení diferenciálních rovnic 22. Diferenciální rovnice se separovanými proměnnými 23. Separovatelná diferenciální rovnice 24. Homogenní diferenciální rovnice 25. Lineární diferenciální rovnice 1. řádu, metoda variace konstanty 26. Cauchyho úloha 27. Lineární diferenciální rovnice 2. řádu s konstantními koeficienty - metoda variace konstant 28. Lineární diferenciální rovnice 2. řádu s konstantními koeficienty - metoda neurčitých koeficientů

E-learning

http://www.studopory.vsb.cz http://mdg.vsb.cz

Další požadavky na studenta

There are no further requirements put on the student.

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0365 ZM Basics of Mathematics Compulsory
714-0366 MI Mathematics I Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

I Integral calculus of functions of one variable Antiderivatives and indefinite integral. Integration of elementary functions, integration by substitutions, integration by parts, integration of rational functions, definite integral and methods of integration, Geometric application of definite integrals. II Differential calculus of functions of two or more real variables Functions of two or more variables, graph, partial derivatives of the 1-st and higher order, total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions. III Ordinary differential equations General, particular and singular solutions, separable homogeneous equations, homogeneous equations, linear differential equations of the first order, method of variation of arbitrary constant, 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian, fundamental system of solutions, 2nd order LDE with constant coefficients - method of variation of arbitrary constants, method of undetermined coefficients, application of differential equations.

Conditions for subject completion

Combined form (validity from: 2012/2013 Winter semester, validity until: 2019/2020 Summer semester)
Task nameType of taskMax. number of points
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20  5
Examination Examination 80 (80) 30
Písemná zkouška Written examination 60  25
Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2010/2011 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2010/2011 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2009/2010 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2009/2010 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Třinec 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Šumperk 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Uherský Brod 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Třinec 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Šumperk 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Uherský Brod 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Třinec 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Šumperk 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Uherský Brod 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Třinec 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - FS - K - cs 2018/2019 Combined Czech Optional FS - Faculty of Mechanical Engineering stu. block