714-0367/03 – Mathematics II (MII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor Ing. Petra Schreiberová, Ph.D. Subject version guarantor Ing. Petra Schreiberová, 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.
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
KOT31 RNDr. Jan Kotůlek, Ph.D.
KRC76 Mgr. Jiří Krček
OTI73 Mgr. Petr Otipka
KAH14 Mgr. Marcela Rabasová, Ph.D.
SKN002 Ing. Petra Schreiberová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time 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

Course-credit -participation on tutorials is obligatory, 20% of absence can be apologized, -elaborate programs, -pass the written tests, Point classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points. Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0 ECTS grade A B C D E F Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0 National grading scheme excellent very good satisfactory failed

E-learning

http://www.studopory.vsb.cz http://www.vsb.cz/714 http://mdg.vsb.cz/wiki/index.php/MatematikaII

Other requirements

more requierements are not

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:

Syllabus of lecture 1 Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions. 2 Integration by substitutions, integration by parts. 3 Integration of rational functions. 4 Definite integral and methods of integration. 5 Geometric application of definite integrals. 6 Differential calculus of functions of two or more real variables. Functions of two or more variables, graph, 7 Partial derivatives of the 1-st and higher order. 8 Total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions. 9 Ordinary differential equations. General, particular and singular solutions. Separable homogeneous equations. 10 Homogeneous equations. Linear differential equations of the first order, method of variation of arbitrary constant. 11 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian,fundamental system of solutions. 12 2nd order LDE with constant coefficients - method of variation of arbitrary constants. 13 2nd order LDE with constant coefficients - method of undetermined coefficients. 14 Application of differential equations Syllabus of tutorial 1 Course of a function of one real variable. 2 Integration by a direct method. Integration by substitution. 3 Integration by substitution. Integration by parts. 4 Integration of rational functions. 5 1st test (basic methods of integration). Definite integrals. 6 Applications of definite integrals. 7 Functions of more variables, domain, partial derivatives. 8 Equation of a tangent plane and a normal to a graph of functions of two variables. Derivation of implicit functions. 9 Extrema of functions. 2nd test (functions of two variables). 10 Differential equations, separable and homogeneous differential equations. 11 Linear differential equations of 1st order. Exact differential equations. 12 2nd order linear differential equations with constant coefficients. 3rd test (differential equations). 13 Method of undetermined coefficients. 14 Application of differential equations.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2018/2019 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2017/2018 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2016/2017 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2013/2014 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2013/2014 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2012/2013 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2012/2013 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2012/2013 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2012/2013 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2011/2012 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2011/2012 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2011/2012 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2011/2012 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2010/2011 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2010/2011 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2010/2011 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2010/2011 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2009/2010 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering P Czech Šumperk 1 Compulsory study plan
2009/2010 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering P Czech Ostrava 1 Compulsory study plan
2009/2010 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2009/2010 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2341) Engineering P Czech Šumperk 1 Compulsory study plan
2008/2009 (B2341) Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2341) Engineering (3708R028) Transport Technology (70) P Czech Ostrava 2 Compulsory study plan
2008/2009 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (60) P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (70) P Czech Ostrava 2 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (50) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (50) P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner