* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code | 230-0230/01 | |||||
---|---|---|---|---|---|---|

Number of ECTS Credits Allocated | 2 ECTS credits | |||||

Type of Course Unit * | Optional | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | ||||||

Semester when the Course Unit is delivered | Summer Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech | |||||

Prerequisites and Co-Requisites | ||||||

Prerequisities | Course Unit Code | Course Unit Title | ||||

230-0201 | Mathematics | |||||

230-0202 | Mathematics II | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

JAR71 | Mgr. Marcela Jarošová, Ph.D. | |||||

Summary | ||||||

Integral calculus of functions of several independent variables: double and triple integrals, line integral of the first and the second kind. | ||||||

Learning Outcomes of the Course Unit | ||||||

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 analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze 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. | ||||||

Course Contents | ||||||

1. Double integral over a rectangular domain and over a general regular domain.
2. Transformation to polar and generalized polar coordinates. 3. Applications of double integrals. 4. Triple integral over a rectangular hexahedron and over a general regular domain. 5. Transformation to cylindrical and generalized cylindrical coordinates. 6. Transformation to spherical and generalized spherical coordinates. 7. Applications of triple integrals. 8. Line integrals. 9. Line integral of a scalar field. 10. Line integral of a vector field. 11. Green’s theorem and the path independence. 12. Applications of line integrals. 13. Applications in the civil engineering. 14. Reserve | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

http://www.studopory.vsb.cz
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf | ||||||

http://www.studopory.vsb.cz
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf | ||||||

Recommended Reading: | ||||||

http://homen.vsb.cz/~kre40/matematika.html#m3
Burda, P. - Doležalová, J.: Integrální počet funkcí více proměnných – Matematika IIIb. Skriptum VŠB, Ostrava 2003. ISBN 80-248-0454-9. Burda, P. - Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB, Ostrava 2002. ISBN 80-248-0028-4. | ||||||

http://homen.vsb.cz/~kre40/matematika.html#m3
Burda, P. - Doležalová, J.: Integrální počet funkcí více proměnných – Matematika IIIb. Skriptum VŠB, Ostrava 2003. ISBN 80-248-0454-9. Burda, P. - Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB, Ostrava 2002. ISBN 80-248-0028-4. | ||||||

Planned learning activities and teaching methods | ||||||

Individual consultations, Tutorials | ||||||

Assesment methods and criteria | ||||||

Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing | |||

Graded credit | Graded credit | 100 | 51 |