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

Subject guarantor | Mgr. Arnošt Žídek, Ph.D. | Subject version guarantor | Mgr. Arnošt Žídek, Ph.D. |

Study level | undergraduate or graduate | ||

Study language | English | ||

Year of introduction | 2010/2011 | Year of cancellation | 2019/2020 |

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

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

Login | Name | Tuitor | Teacher giving lectures |

ZID76 | Mgr. Arnošt Žídek, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

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

Goals and competence
Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.
Students should learn how to
analyse problems,
distinguish between important and unimportant,
suggest a method of solution,
verify each step of a method,
generalize achieved results,
analyse correctness of achieved results with respect to given conditions,
apply these methods while solving technical problems,
understand that mathematical methods and theoretical advancements
outreach the field mathematics.
It is necessary to complete Mathematics 1 and Mathematics 2 courses or their
equivalents.

Lectures

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.
- 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.

http://mdg.vsb.cz/wiki/public/Double_Integral.pdf

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.

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

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

ECTS - MechEng - Bachelor Studies | 2018/2019 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

FBI_ECTS | 2018/2019 | Full-time | Czech | Optional | 010 - Faculty of Safety Engineering - Dean's Office | stu. block | |||

FMMI | 2018/2019 | Full-time | English | Compulsory | 601 - Study Office | stu. block | |||

ECTS FCE Bc-Mgr | 2018/2019 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2017/2018 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

FBI_ECTS | 2017/2018 | Full-time | English | Optional | 010 - Faculty of Safety Engineering - Dean's Office | stu. block | |||

USP | 2017/2018 | Full-time | English | Optional | USP - University Study Programmes | stu. block | |||

FBI_ECTS | 2017/2018 | Full-time | Czech | Optional | 010 - Faculty of Safety Engineering - Dean's Office | stu. block | |||

ECTS FCE Bc-Mgr | 2017/2018 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

FMMI | 2017/2018 | Full-time | English | Compulsory | 601 - Study Office | stu. block | |||

ECTS FMG-VSB | 2017/2018 | Full-time | English | Optional | 501 - Study Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2016/2017 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

FMMI | 2016/2017 | Full-time | English | Compulsory | 601 - Study Office | stu. block | |||

ECTS FCE Bc-Mgr | 2016/2017 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

FBI_ECTS | 2016/2017 | Full-time | Czech | Optional | 010 - Faculty of Safety Engineering - Dean's Office | stu. block | |||

USP | 2016/2017 | Full-time | English | Optional | USP - University Study Programmes | stu. block | |||

ECTS FMG-VSB | 2016/2017 | Full-time | English | Optional | 501 - Study Office | stu. block | |||

USP | 2015/2016 | Full-time | English | Optional | USP - University Study Programmes | stu. block | |||

V - ECTS - VSB | 2015/2016 | Full-time | English | Optional | 401 - Study Office | stu. block | |||

FMMI | 2015/2016 | Full-time | English | Compulsory | 601 - Study Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2015/2016 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

FBI_ECTS | 2015/2016 | Full-time | Czech | Optional | 010 - Faculty of Safety Engineering - Dean's Office | stu. block | |||

ECTS FMG - VSB | 2015/2016 | Full-time | Czech | Optional | 501 - Study Office | stu. block | |||

V - ECTS - VSB | 2014/2015 | Full-time | Czech | Optional | 401 - Study Office | stu. block | |||

FBI_ECTS | 2014/2015 | Full-time | Czech | Optional | 010 - Faculty of Safety Engineering - Dean's Office | stu. block | |||

FMMI_N | 2014/2015 | Full-time | Czech | Compulsory | 601 - Study Office | stu. block | |||

USP | 2014/2015 | Full-time | Czech | Optional | USP - University Study Programmes | stu. block | |||

O - ECTS FMG - Bc. | 2014/2015 | Full-time | Czech | Optional | 501 - Study Office | stu. block | |||

ECTS - MechEng | 2014/2015 | Full-time | Czech | Choice-compulsory | 301 - Study and International Office | stu. block | |||

V - ECTS - VSB | 2013/2014 | Full-time | Czech | Optional | 401 - Study Office | stu. block | |||

O - ECTS FMG - Bc. | 2013/2014 | Full-time | Czech | Optional | 501 - Study Office | stu. block | |||

USP | 2013/2014 | Full-time | Czech | Optional | USP - University Study Programmes | stu. block | |||

FMMI | 2013/2014 | Full-time | Czech | Compulsory | 601 - Study Office | stu. block | |||

ECTS - MechEng | 2013/2014 | Full-time | Czech | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS - MechEng | 2012/2013 | Full-time | Czech | Choice-compulsory | 301 - Study and International Office | stu. block | |||

O - ECTS FMG - Bc. | 2012/2013 | Full-time | Czech | Optional | 501 - Study Office | stu. block | |||

FMMI | 2012/2013 | Full-time | Czech | Compulsory | 601 - Study Office | stu. block | |||

USP | 2012/2013 | Full-time | Czech | Optional | USP - University Study Programmes | stu. block | |||

V - ECTS - VSB | 2012/2013 | Full-time | Czech | Optional | 401 - Study Office | stu. block |