310-3141/03 – Mathematics IV (MIV)

Gurantor department	Department of Mathematics and Descriptive Geometry	Credits	5
Subject guarantor	prof. RNDr. Radek Kučera, Ph.D.	Subject version guarantor	prof. RNDr. Radek Kučera, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	1	Semester	winter
		Study language	English
Year of introduction	2019/2020	Year of cancellation
Intended for the faculties	FS	Intended for study types	Follow-up Master

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
JHA0009	Adil Jhangeer
KRC76	Mgr. Jiří Krček, Ph.D.
KUC14	prof. RNDr. Radek Kučera, Ph.D.

Extent of instruction for forms of study
Form of study	Way 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

Additional study materials

Study supports in the EduDocs system

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 name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. 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

Valid from	Valid until	Mandatory attendence participation
Dec 6, 2018 2:09:17 PM	Feb 13, 2023 9:35:19 AM	80%

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.

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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

Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Year	Type of duty
2027/2028	(N0715A270034) Applied Mechanics		P	English	Ostrava	1	Compulsory	study plan
2026/2027	(N0715A270034) Applied Mechanics		P	English	Ostrava	1	Compulsory	study plan
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2025/2026	(N0715A270033) Applied Mechanics		P	Czech	Ostrava	1	Compulsory	study plan
2025/2026	(N0715A270037) Engineering Design	(S01) Transport and process equipment	P	Czech	Ostrava	1	Compulsory	study plan
2025/2026	(N0715A270037) Engineering Design	(S02) Production Machines and Design	P	Czech	Ostrava	1	Compulsory	study plan
2025/2026	(N0715A270037) Engineering Design	(S03) Engineering Diagnostics	P	Czech	Ostrava	1	Compulsory	study plan
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2025/2026	(N0715A270037) Engineering Design	(S05) Design of industrial products	P	Czech	Ostrava	1	Compulsory	study plan
2025/2026	(N0715A270037) Engineering Design	(S06) Construction of Mechanical Parts	P	Czech	Ostrava	1	Compulsory	study plan
2025/2026	(N0713A070003) Energy Engineering		P	English	Ostrava	1	Compulsory	study plan
2025/2026	(N0714A270012) Control of Machines and Processes		P	English	Ostrava	1	Compulsory	study plan
2025/2026	(N0715A270009) Industrial Engineering		P	English	Ostrava	1	Compulsory	study plan
2025/2026	(N0715A270022) Mechanical Engineering Technology		P	English	Ostrava	1	Compulsory	study plan
2025/2026	(N0788A270010) Additive technology		P	English	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270034) Applied Mechanics		P	English	Ostrava	1	Compulsory	study plan
2024/2025	(N0713A070003) Energy Engineering		P	English	Ostrava	1	Compulsory	study plan
2024/2025	(N0714A270012) Control of Machines and Processes		P	English	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270009) Industrial Engineering		P	English	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270022) Mechanical Engineering Technology		P	English	Ostrava	1	Compulsory	study plan
2024/2025	(N0788A270010) Additive technology		P	English	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270033) Applied Mechanics		P	Czech	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270037) Engineering Design	(S05) Design of industrial products	P	Czech	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270037) Engineering Design	(S03) Engineering Diagnostics	P	Czech	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270037) Engineering Design	(S06) Construction of Mechanical Parts	P	Czech	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270037) Engineering Design	(S02) Production Machines and Design	P	Czech	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270037) Engineering Design	(S04) Earthwork and Building Machines	P	Czech	Ostrava	1	Compulsory	study plan
2024/2025	(N0715A270037) Engineering Design	(S01) Transport and process equipment	P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270034) Applied Mechanics		P	English	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270033) Applied Mechanics		P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0713A070003) Energy Engineering		P	English	Ostrava	1	Compulsory	study plan
2023/2024	(N0714A270012) Control of Machines and Processes		P	English	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270022) Mechanical Engineering Technology		P	English	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270037) Engineering Design	(S06) Construction of Mechanical Parts	P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270037) Engineering Design	(S04) Earthwork and Building Machines	P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270037) Engineering Design	(S02) Production Machines and Design	P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270037) Engineering Design	(S01) Transport and process equipment	P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270037) Engineering Design	(S05) Design of industrial products	P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270037) Engineering Design	(S03) Engineering Diagnostics	P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(N0715A270009) Industrial Engineering		P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270034) Applied Mechanics		P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270033) Applied Mechanics		P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0713A070003) Energy Engineering		P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270037) Engineering Design	(S01) Transport and process equipment	P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270037) Engineering Design	(S02) Production Machines and Design	P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270037) Engineering Design	(S03) Engineering Diagnostics	P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270037) Engineering Design	(S04) Earthwork and Building Machines	P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270037) Engineering Design	(S05) Design of industrial products	P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270037) Engineering Design	(S06) Construction of Mechanical Parts	P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(N0714A270012) Control of Machines and Processes		P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270022) Mechanical Engineering Technology		P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N2301) Mechanical Engineering	(3901T003) Applied Mechanics	P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N2301) Mechanical Engineering	(2302T006) Energy Engineering	P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0715A270009) Industrial Engineering		P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0719A270010) Robotics	(S01) Designing of Robotic Workcells	P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0719A270010) Robotics	(S03) Service Robotics	P	English	Ostrava	1	Compulsory	study plan
2022/2023	(N0719A270010) Robotics	(S02) Mechanical Design of Robotic Systems	P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N0713A070003) Energy Engineering		P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270009) Industrial Engineering		P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270034) Applied Mechanics		P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270033) Applied Mechanics		P	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270022) Mechanical Engineering Technology		P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N0714A270012) Control of Machines and Processes		P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N2301) Mechanical Engineering	(3901T003) Applied Mechanics	P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N2301) Mechanical Engineering	(2302T006) Energy Engineering	P	English	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270037) Engineering Design	(S06) Construction of Mechanical Parts	P	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270037) Engineering Design	(S01) Transport and process equipment	P	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270037) Engineering Design	(S02) Production Machines and Design	P	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270037) Engineering Design	(S05) Design of industrial products	P	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270037) Engineering Design	(S04) Earthwork and Building Machines	P	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(N0715A270037) Engineering Design	(S03) Engineering Diagnostics	P	Czech	Ostrava	1	Compulsory	study plan
2020/2021	(N0713A070003) Energy Engineering		P	English	Ostrava	1	Compulsory	study plan
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
2019/2020	(N0713A070003) Energy Engineering		P	English	Ostrava	1	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction