310-3141/03 – 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 languageEnglish
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
Full-time Credit and Examination 2+3

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

Seminar Attending the seminar is required, only 20 % of missed lessons will be excused. It is also necessary to elaborate the home project in a form specified by the lecturer and a student is awarded 5 points for the project. Several tests will be carried out during the semester, a student can acquire up to 15 points. Examination The exam consists of two parts: I) Practical part - tests the ability of solving practical problems. (60 points is a maximum, but at least 20 points are necessary) II) Theoretical part - examines the understanding of the underlying theoretical concepts. (20 points is a maximum, but at least 5 points are necessary)

E-learning

http://www.studopory.vsb.cz (in Czech language) http://lms.vsb.cz

Other requirements

No more requirements are put on the student.

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

Full-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
                Practical part Written examination 60  25
                Theoretical part Oral examination 20  5
Mandatory attendence participation: The mandatory participation is 80%. To complete the credit, students must successfully pass the credit test. On the basis of a successfully completed credit, they can take an exam, which will consist of a practical and a theoretical part.

Show history

Conditions for subject completion and attendance at the exercises within ISP: I order to complete the credit, students submit and defend a set of solved examples assigned by the teacher. On the basis of a successfully completed credit, they can take an exam, which will consist of a practical and a theoretical part.

Show history

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2020/2021 (N0715A270009) Industrial Engineering P English Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2302T006) Energy Engineering P English Ostrava 1 Compulsory study plan
2020/2021 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270022) Mechanical Engineering Technology P English Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2302T006) Energy Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (N0715A270009) Industrial Engineering P English Ostrava 1 Compulsory study plan
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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2023/2024 Winter
2022/2023 Winter
2021/2022 Winter