# 714-2666/01 – Mathematics II (M II)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 6 Subject guarantor Mgr. Jiří Vrbický, Ph.D. Subject version guarantor Mgr. Jiří Vrbický, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2014/2015 Year of cancellation 2018/2019 Intended for the faculties FMT Intended for study types Bachelor
Instruction secured by
H1O40 Mgr. Iveta Cholevová, Ph.D.
KRC76 Mgr. Jiří Krček
LUN44 Mgr. Milena Luňáčková, Ph.D.
MOR74 Mgr. Zuzana Morávková, Ph.D.
VRB50 Mgr. Jiří Vrbický, 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 3+3
Combined Credit and Examination 20+0

### Subject aims expressed by acquired skills and competences

The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to: analyze problems, suggest a method of solution, analyze correctness of achieved results with respect to given conditions, aply these methods while solving technical problems.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Differential calculus of functions of several independent variables. 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. Ordinary differential equations of the first and the second order.

### Compulsory literature:

James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456. James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6.

### Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1.

### 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://mdg.vsb.cz/M/

No special requirements.

### Prerequisities

Subject codeAbbreviationTitleRequirement
714-2665 M I Mathematics I Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1 Differential calculus of functions of two or more real variables. Functions of two or more variables, graph, 2 Partial derivatives of the 1-st and higher order. 3 Total differential of functions of two variables, tangent plane and normal to a surface, extrema of functions. 4 Integral calculus of functions of one variable. Antiderivatives and indefinite integral. Integration of elementary functions. 5 Integration by substitutions, integration by parts. 6 Integration of rational functions. 7 Definite integral and methods of integration. 8 Geometric and physical application of definite integrals. 9 Ordinary differential equations. General, particular and singular solutions. Separable equations. 10 Homogeneous equations. Exact 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

### Conditions for subject completion

Combined form (validity from: 2014/2015 Summer semester, validity until: 2018/2019 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20  5
Examination Examination 80 (80) 30
písemka Written test 60  25
teorie 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 (B3923) Materials Engineering (3911R034) Materials and Technologies for Automobile Industry P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3923) Materials Engineering (3911R033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3909) Process Engineering (3909R014) Process Engineering and Quality Control Methods P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3909) Process Engineering (2805R002) Chemistry and Technology of Environmental Protection P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry P Czech Ostrava 1 Compulsory study plan
2018/2019 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management P Czech Ostrava 1 Compulsory study plan
2018/2019 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies K Czech Ostrava 1 Compulsory study plan
2018/2019 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials K Czech Ostrava 1 Compulsory study plan
2018/2019 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials K Czech Ostrava 1 Compulsory study plan
2018/2019 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2018/2019 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry K Czech Ostrava 1 Compulsory study plan
2018/2019 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3923) Materials Engineering (3911R034) Materials and Technologies for Automobile Industry P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3923) Materials Engineering (3911R033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3909) Process Engineering (3909R014) Process Engineering and Quality Control Methods P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3909) Process Engineering (2805R002) Chemistry and Technology of Environmental Protection P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2017/2018 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry P Czech Ostrava 1 Compulsory study plan
2017/2018 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies K Czech Ostrava 1 Compulsory study plan
2017/2018 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3923) Materials Engineering (3911R034) Materials and Technologies for Automobile Industry P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3923) Materials Engineering (3911R033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3909) Process Engineering (3909R014) Process Engineering and Quality Control Methods P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3909) Process Engineering (2805R002) Chemistry and Technology of Environmental Protection P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2016/2017 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry P Czech Ostrava 1 Compulsory study plan
2016/2017 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies K Czech Ostrava 1 Compulsory study plan
2016/2017 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies K Czech Ostrava 1 Compulsory study plan
2015/2016 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials P Czech Ostrava 1 Compulsory study plan
2015/2016 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3923) Materials Engineering (3911R034) Materials and Technologies for Automobile Industry P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3923) Materials Engineering (3911R033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3909) Process Engineering (3909R014) Process Engineering and Quality Control Methods P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3909) Process Engineering (2805R002) Chemistry and Technology of Environmental Protection P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management P Czech Ostrava 1 Compulsory study plan
2015/2016 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3909) Process Engineering (3909R014) Process Engineering and Quality Control Methods P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2014/2015 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry P Czech Ostrava 1 Compulsory study plan
2014/2015 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies K Czech Ostrava 1 Compulsory study plan
2014/2015 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry K Czech Ostrava 1 Compulsory study plan
2014/2015 (B3909) Process Engineering (2805R002) Chemistry and Technology of Environmental Protection P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner