714-0211/02 – Mathematics IV (MgrM4)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | Mgr. Jiří Krček | Subject version guarantor | Mgr. Jiří Krček |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2015/2016 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FAST | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
Integral calculus of functions of several independent variables: double and triple integrals, vector analysis, line integral of the first and the second kind.
Compulsory literature:
http://www.studopory.vsb.cz
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf
Recommended literature:
Way of continuous check of knowledge in the course of semester
E-learning
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. 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. Vector fields. Divergence and rotation of vector fields. 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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction