Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |

Subject guarantor | Mgr. Jiří Krček | Subject version guarantor | Mgr. Jiří Krček |

Study level | undergraduate or graduate | ||

Study language | English | ||

Year of introduction | 2019/2020 | Year of cancellation | |

Intended for the faculties | FBI, FAST, HGF, FMT, FS, FEI | Intended for study types | Bachelor, Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

KRC76 | Mgr. Jiří Krček |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

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 and line integrals and with basic concepts from field theory.

Lectures

Seminars

Individual consultations

Other activities

Mathematics 3 is connected with Mathematics 1,2.
We have to stress that student can enrol in this course only if he passed the course Mathematics 1 and 2 or an equivalent course.
- Integral calculus of functions of more than one variable
- Double and volume integral. Fubini's Theorem: integrating over regular regions.
- Transformation of variables, polar, cylindrical and spherical coordinates.
- Practical applications of double and volume integral.
- Theory of the field. Scalar and vector fields.
- Curves and their orientation, line integral of a scalar function and its geometrical applications.
- Line integral of a vector function and its physical applications.
- Path independence, Green's theorem.

Lectures in English on school Moodle system - lms.vsb.cz

Neustupa J., Kračmar S.: Mathematics II. ČVUT, Praha 1998.
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language)

Passing the course, requirements
Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-elaborate programs,
-pass the written tests,
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 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 50 - 0
National grading scheme excellent very good satisfactory failed
List of theoretical questions
1. Definition of the double integral over rectangular region.
2. Dirichlet's Theorem for calculation of the double integral over rectangular region.
3. Elementary region relative to the x-axis.
4. Elementary region relative to the y-axis.
5. Fubini's Theorem for calculation of the double integral over regular region.
6. Transformation of the double integral to the polar coordinates.
7. Regular mapping and its Jacobian. Derive Jacobian for the transformation to the polar coordinates.
8. Transformation to generalized polar coordinates.
9. Calculation of the volume of perpendicular cylinder over the region (using double integral).
10. Calculation of the size of a regular plane area (using double integral).
11. Calculation of the size of an area over the region (using double integral).
12. Calculation of coordinates of center of mass (using double integral).
13. Calculation of moments of inertia about the x- (y-) axis. (using double integral).
14. Definition of the volume integral on a rectangular region.
15. Dirichlet's Theorem for calculation of the volume integral on a rectangular region.
16. Elementary region relative to the xy-plane.
17. Elementary region relative to the xz-plane.
18. Elementary region relative to the yz-plane.
19. Fubini's Theorem for calculation of the volume integral on a regular region.
20. Calculation of the volume integral by transformation to the cylindrical coordinates.
21. Calculation of the volume integral by transformation to the spherical coordinates.
22. Derive Jacobian for the transformation to the cylindrical coordinates.
23. Derive Jacobian for the transformation to the spherical coordinates.
24. Calculation of the volume of regular 3-D region (using volume integral).
25. Calculation of static moments of 3-D region with about the coordinate planes (using volume integral).
26. Calculation of moments of inertia of 3-D region about the coordinate axis (using volume integral).
27. Calculation of the center of mass of 3-D region (using volume integral).
28. Equation of the curve in R^3. Positive and negative orientation of a closed curve.
29. Line integral of a scalar function and its calculation.
30. Geometrical meaning of a line integral of a scalar function.
31. Line integral of a vector function and its calculation.
32. Physical meaning of a line integral of a vector function.
33. Green's Theorem.
34. Calculation of the size of an area using line integral.

http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language)
http://mdg.vsb.cz

No more requirements are put on the student.

Subject has no prerequisities.

Subject has no co-requisities.

Course description (weekly lessons):
1. Double integral over rectangular region.
2. Double integral over regular region. Fubini's Theorem.
3. Transformation of variables. Mapping and its Jacobian. Polar coordinates.
4. Practical applications of double integral.
5. Volume integral over rectangular region.
6. Volume integral over regular region.
7. Transformation to the cylindrical coordinates.
8. Transformation to the spherical coordinates.
9. Practical applications of volume integral.
10. Curves in R^3. Their equations and orientation of closed curves.
11. Line integral of a scalar function.
12. Line integral of a vector function.
13. Path independence. Green's Theorem.
14. Practical applications of line integrals of both kinds.

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) | 30 | 3 |

Writing test | Written test | 60 | 25 | |

Theoretical part of the exam | Oral examination | 20 | 5 |

Show history

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

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty |
---|

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

ECTS - MechEng - Bachelor Studies | 2022/2023 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS Bc.-Mgr. | 2022/2023 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

FMT+9360 | 2021/2022 | Full-time | English | Optional | 600 - Faculty of Materials Science and Technology - Dean's Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2021/2022 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS Bc.-Mgr. | 2021/2022 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

FMT+9360 | 2020/2021 | Full-time | English | Optional | 600 - Faculty of Materials Science and Technology - Dean's Office | stu. block | |||

ECTS FCE Bc-Mgr | 2020/2021 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2020/2021 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS FCE Bc-Mgr | 2019/2020 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

Additional Subjects | 2019/2020 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

FMST | 2019/2020 | Full-time | English | Compulsory | 601 - Study Office | stu. block |

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