# 310-2212/01 – Mathematics II (M II)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 6 Subject guarantor Mgr. Zuzana Morávková, Ph.D. Subject version guarantor Mgr. Zuzana Morávková, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FMT Intended for study types Bachelor
Instruction secured by
KRC76 Mgr. Jiří Krček
MOR74 Mgr. Zuzana Morávková, Ph.D.
VRB50 Mgr. Jiří Vrbický, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Part-time 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:

[1] KREML, P: Mathematics II, Ostrava 2005, 80-248-0798-X. http://mdg.vsb.cz/portal/en/Mathematics2.pdf [2] JAMES, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456.

### Recommended literature:

[1] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6. [2] 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://mdg.vsb.cz/portal/m2/

### Other requirements

No special requirements.

### Prerequisities

Subject codeAbbreviationTitleRequirement
310-2211 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

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30
písemka Written test 60  25
teorie Oral examination 20  5
Mandatory attendence parzicipation: 80%

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (B0712A130004) Chemical and environmental engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0713A070001) Thermal energetics engineering K Czech Ostrava 1 Compulsory study plan
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2021/2022 (B0715A270006) Modern Production and Processing of Metallic Materials P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270006) Modern Production and Processing of Metallic Materials K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270007) Materials and technologies for the automotive industry P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0488A270001) Quality Management and Control of Industrial Systems (S01) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0488A270001) Quality Management and Control of Industrial Systems (S02) Quality Management P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0488A270001) Quality Management and Control of Industrial Systems (S01) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0488A270001) Quality Management and Control of Industrial Systems (S03) Computer Control Systems in Industry P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0488A270001) Quality Management and Control of Industrial Systems (S02) Quality Management K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0488A270001) Quality Management and Control of Industrial Systems (S03) Computer Control Systems in Industry K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270004) Materials Engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270004) Materials Engineering K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270005) Materials technologies and recycling K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0715A270005) Materials technologies and recycling P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0488A270001) Quality Management and Control of Industrial Systems (S01) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0488A270001) Quality Management and Control of Industrial Systems (S02) Quality Management P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0488A270001) Quality Management and Control of Industrial Systems (S03) Computer Control Systems in Industry P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0488A270001) Quality Management and Control of Industrial Systems (S03) Computer Control Systems in Industry K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0488A270001) Quality Management and Control of Industrial Systems (S01) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0488A270001) Quality Management and Control of Industrial Systems (S02) Quality Management K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0712A130004) Chemical and environmental engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0713A070001) Thermal energetics engineering K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0713A070001) Thermal energetics engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270004) Materials Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270004) Materials Engineering K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270005) Materials technologies and recycling P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270005) Materials technologies and recycling K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270006) Modern Production and Processing of Metallic Materials K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270006) Modern Production and Processing of Metallic Materials P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270007) Materials and technologies for the automotive industry P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3923) Materials Engineering (3911R034) Materials and Technologies for Automobile Industry P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3923) Materials Engineering (3911R033) Material Recycling P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3909) Process Engineering (3909R014) Process Engineering and Quality Control Methods P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3909) Process Engineering (2805R002) Chemistry and Technology of Environmental Protection P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3923) Materials Engineering (3911R036) Advanced Engineering Materials P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2109) Metallurgical Engineering (2109R038) Modern Metallurgical Technologies P Czech Ostrava 1 Compulsory study plan
2019/2020 (B2109) Metallurgical Engineering (2109R039) Thermal Engineering and Ceramic Materials P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3922) Economics and Management of Industrial Systems (6208R123) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3922) Economics and Management of Industrial Systems (3902R040) Automation and Computing in Industry P Czech Ostrava 1 Compulsory study plan
2019/2020 (B3922) Economics and Management of Industrial Systems (3902R062) Quality Management P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0488A270001) Quality Management and Control of Industrial Systems (S01) Economics and Management in Industry P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0488A270001) Quality Management and Control of Industrial Systems (S01) Economics and Management in Industry K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0488A270001) Quality Management and Control of Industrial Systems (S02) Quality Management P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270007) Materials and technologies for the automotive industry P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0713A070001) Thermal energetics engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0712A130004) Chemical and environmental engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0488A270001) Quality Management and Control of Industrial Systems (S02) Quality Management K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270004) Materials Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270004) Materials Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0488A270001) Quality Management and Control of Industrial Systems (S03) Computer Control Systems in Industry P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270006) Modern Production and Processing of Metallic Materials P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270006) Modern Production and Processing of Metallic Materials K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0713A070001) Thermal energetics engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270005) Materials technologies and recycling P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0488A270001) Quality Management and Control of Industrial Systems (S03) Computer Control Systems in Industry K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270005) Materials technologies and recycling K Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - FMT - P - cs 2020/2021 Full-time Czech Optional FMT - Faculty of Materials Science and Technology stu. block