714-0239/01 – Repetition of Mathematics 4 (Repet 4)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 1 |
| Subject guarantor | Mgr. Jiří Krček | Subject version guarantor | Mgr. Jiří Krček |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2016/2017 | 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 an 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.
Teaching methods
Tutorials
Summary
Repetition of Mathematics 4 is intended for students who, for whatever reasons, fail the exam of Mathematics IV and are interested in passing this exam. Its content essentially coincides with the content of the course Mathematics IV. The aim is to enable better understanding of mathematics by the solving of concrete examples and problems. Repetition will focus on the practical part of the exam and there will be solved examples matching the written part of the exam.
Compulsory literature:
Trench, W: Introduction to Real Analysis. http://ramanujan.math.trinity.edu/wtrench/texts/index.shtml (free download)
Recommended literature:
Trench, W: Introduction to Real Analysis. http://ramanujan.math.trinity.edu/wtrench/texts/index.shtml (free download)
Way of continuous check of knowledge in the course of semester
The course is optional and requires the active participation of students registered. Participation on tutorials is obligatory, 20% of absence can be apologized.
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.
14. Reserve.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.