310-3141/02 – Mathematics IV (MIV)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFSIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 16+4

Subject aims expressed by acquired skills and competences

The aim of the subject is to extend the mathematical topics from the bachelor study. Students will become familiar with systems of linear differential equations, double, triple, curve, and surface integrals and with basic concepts from field theory.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions, Euler method for homogeneous systems of n equations for n functions. Integral calculus of functions of several independent variables: two-dimensional integrals, three-dimensional integrals, vector analysis, line integral of the first and the second kind, surface integral of the first and second kind.

Compulsory literature:

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990. ISBN 0-669-21145-1 [2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

Recommended literature:

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990, ISBN 0-669-21145-1 [2] 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 účast na konzultacích v rozsahu 50 - 100 % může student získat 10 – 20 bodů, v případě účasti nižší může student získat 5 bodů za zpracování zadaného programu. Celkem maximálně 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

E-learning

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

Other requirements

There are no more requirements.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions. 2 Euler method for homogeneous systems of n equations for n functions. 3 Variation of constants. 4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2. 5 Transformation - polar coordinates, geometrical and physical applications. 6 Three-dimensional integrals on coordinate cube, on bounded subset of R3. 7 Transformation - cylindrical and spherical coordinates, geometrical and physical applications. 8 Vector analysis, gradient. 9 Divergence, rotation. 10 Line integral of the first and of the second kind. 11 Green´s theorem, potential. 12 Geometrical and physical applications. 13 Surface integral of the first and of the second kind. 14 Stokes and Gauss-Ostrogradski theorem.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter 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) 31 3
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence participation:

Show history

Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

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2022/2023 (N0715A270037) Engineering Design (S05) Design of industrial products K Czech Ostrava 1 Compulsory study plan
2022/2023 (N1041A040002) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3901T003) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
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2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Compulsory study plan
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2021/2022 (N0714A270011) Control of Machines and Processes K Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3901T003) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3902T004) Automatic Control and Engineering Informatics K Czech Ostrava 1 Compulsory study plan
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2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines K Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (2301T013) Robotics K Czech Ostrava 1 Compulsory study plan
2021/2022 (N0713A070002) Energy Engineering K Czech Ostrava 1 Compulsory study plan
2021/2022 (N1041A040002) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270037) Engineering Design (S03) Engineering Diagnostics K Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270037) Engineering Design (S04) Earthwork and Building Machines K Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270037) Engineering Design (S01) Transport and process equipment K Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270037) Engineering Design (S05) Design of industrial products K Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270037) Engineering Design (S02) Production Machines and Design K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0713A070002) Energy Engineering K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270008) Industrial Engineering K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270007) Mechanical Engineering Technology K Czech Ostrava 1 Compulsory study plan
2020/2021 (N1041A040002) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3901T003) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3902T004) Automatic Control and Engineering Informatics K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2302T043) Hydraulics and Pneumatics K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment K Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines K Czech Ostrava 1 Compulsory study plan
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2020/2021 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (20) Road Transport K Czech Ostrava 1 Compulsory study plan
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2020/2021 (N2301) Mechanical Engineering (2301T013) Robotics K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270033) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0714A270011) Control of Machines and Processes K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3902T004) Automatic Control and Engineering Informatics K Czech Ostrava 1 Compulsory study plan
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2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (20) Road Transport K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (30) Transport Technology K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2302T043) Hydraulics and Pneumatics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2303T002) Mechanical Engineering Technology K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2302T006) Energy Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2301T013) Robotics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0715A270008) Industrial Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0715A270007) Mechanical Engineering Technology K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0713A070002) Energy Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (N1041A040002) Transport Systems and Equipment 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 - FS - K - cs 2020/2021 Part-time Czech Optional FS - Faculty of Mechanical Engineering stu. block

Assessment of instruction



2021/2022 Winter
2020/2021 Winter
2019/2020 Winter