# 310-3141/01 – 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 Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FS Intended for study types Follow-up Master
Instruction secured by
KRC76 Mgr. Jiří Krček
KUC14 prof. RNDr. Radek Kučera, Ph.D.
RIE0053 Mgr. Tomáš Riemel
SWA0013 RNDr. Martin Swaczyna, Ph.D.
SVO19 Mgr. Ivona Tomečková, 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

Zápočet: Účast ve cvičení je povinná, 20 % neúčasti lze omluvit - za splnění podmínek získá student 2 b., odevzdání programů zadaných vedoucím cvičení v předepsané úpravě, absolvování 3 písemných testů po 6 bodech - za testy lze získat 0 - 18 b. 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

Active participation in exercises.

### 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

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (N0713A070002) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0714A270011) Control of Machines and Processes P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0715A270007) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0715A270008) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0715A270035) Hydraulics and pneumatics 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
2024/2025 (N0788A270009) Additive technology P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0719A270009) Robotics (S02) Mechanical Design of Robotic Systems P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0719A270009) Robotics (S03) Service Robotics P Czech Ostrava 1 Compulsory study plan
2024/2025 (N0719A270009) Robotics (S01) Designing of Robotic Workcells P Czech Ostrava 1 Compulsory study plan
2024/2025 (N1041A040002) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0713A070002) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0714A270011) Control of Machines and Processes P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0715A270007) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0715A270008) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0715A270035) Hydraulics and pneumatics P Czech 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 (N0719A270009) Robotics (S02) Mechanical Design of Robotic Systems P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0719A270009) Robotics (S03) Service Robotics P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0719A270009) Robotics (S01) Designing of Robotic Workcells P Czech Ostrava 1 Compulsory study plan
2023/2024 (N1041A040002) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0788A270009) Additive technology P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0713A070002) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0714A270011) Control of Machines and Processes P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0715A270007) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0715A270008) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0715A270035) Hydraulics and pneumatics P Czech 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 (N0719A270009) Robotics (S01) Designing of Robotic Workcells P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0719A270009) Robotics (S02) Mechanical Design of Robotic Systems P Czech Ostrava 1 Compulsory study plan
2022/2023 (N0719A270009) Robotics (S03) Service Robotics P Czech Ostrava 1 Compulsory study plan
2022/2023 (N1041A040002) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3902T004) Automatic Control and Engineering Informatics P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (2302T043) Hydraulics and Pneumatics P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (60) Design of industrial products P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines P Czech Ostrava 1 Compulsory study plan
2022/2023 (N2301) Mechanical Engineering (2301T013) Robotics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270007) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270008) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270035) Hydraulics and pneumatics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0714A270011) Control of Machines and Processes P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3902T004) Automatic Control and Engineering Informatics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (2302T043) Hydraulics and Pneumatics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (60) Design of industrial products P Czech Ostrava 1 Compulsory study plan
2021/2022 (N2301) Mechanical Engineering (2301T013) Robotics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0719A270009) Robotics (S01) Designing of Robotic Workcells P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0719A270009) Robotics (S02) Mechanical Design of Robotic Systems P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0719A270009) Robotics (S03) Service Robotics P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0713A070002) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (N1041A040002) Transport Systems and Equipment P Czech 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 (N0713A070002) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270008) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270007) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2020/2021 (N1041A040002) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3902T004) Automatic Control and Engineering Informatics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2302T043) Hydraulics and Pneumatics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (60) Design of industrial products P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (6208T116) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2303T002) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2302T006) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (10) Rail Transport P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (20) Road Transport P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (30) Transport Technology P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (40) Air Transport P Czech Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2301T013) Robotics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0714A270011) Control of Machines and Processes P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3902T004) Automatic Control and Engineering Informatics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (10) Rail Transport P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (20) Road Transport P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (30) Transport Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (40) Air Transport P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2302T043) Hydraulics and Pneumatics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (35) Transport Equipment and Material Handling P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (40) Design of Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (72) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (20) Production Machines and Equipment P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (70) Earth, Mining and Building Machines P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (6208T116) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2303T002) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2302T006) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (60) Design of industrial products P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2301T013) Robotics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0713A070002) Energy Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0715A270007) Mechanical Engineering Technology P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0715A270008) Industrial Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (N1041A040002) Transport Systems and Equipment P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner