310-2212/01 – Mathematics II (M II)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits6
Subject guarantorMgr. Petr Otipka, Ph.D.Subject version guarantorMgr. Petr Otipka, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
LAM0028 RNDr. Alžběta Lampartová
OTI73 Mgr. Petr Otipka, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
SWA0013 RNDr. Martin Swaczyna, 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

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:

[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, -pass the written three tests Point classification: 15-35 points. Exam Practical part of an exam is classified by 0 - 55 points. Practical part is successful if student obtains at least 20 points. Theoretical part of the exam is classified by 0 - 10 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

https://lms.vsb.cz/

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, method of undetermined coefficients. 13 Application of differential equations

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester, validity until: 2022/2023 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80 (80) 30 3
                písemka Written test 60  25
                teorie Oral examination 20  5
Mandatory attendence participation: 80%

Show history

Conditions for subject completion and attendance at the exercises within ISP: In order to complete credit, students submit homework and pass test. Participation on the lessons is not required. Based on a successfully completed credit, they can pass the exam.

Show history

Occurrence in study plans

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2021/2022 (B0715A270006) Modern Production and Processing of Metallic Materials P Czech Ostrava 1 Compulsory study plan
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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
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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
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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

Assessment of instruction



2023/2024 Summer
2022/2023 Summer
2021/2022 Summer
2020/2021 Summer
2019/2020 Summer