230-0326/01 – Repetition of Engineering Mathematics (Repet IM)
| Gurantor department | Department of Mathematics | Credits | 1 |
| Subject guarantor | Mgr. Jakub Stryja, Ph.D. | Subject version guarantor | Mgr. Jakub Stryja, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2022/2023 | Year of cancellation | |
| Intended for the faculties | FBI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
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 and verify each step of an algorithm,
generalize achieved results,
analyze correctness of results with respect to given conditions,
apply these methods while solving technical problems.
Teaching methods
Tutorials
Summary
Repetition of Engineering Mathematics is intended for students who, for whatever reasons, fail the exam of Engineering Mathematics and are interested in passing this exam. Its content essentially coincides with the content of the course Engineering Mathematics. Repetition will focus on the practical part of the exam.
Compulsory literature:
Recommended literature:
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992.
ISBN 0-201-1805456
Way of continuous check of knowledge in the course of semester
Course-credit: participation on tutorials is obligatory, 20% of absence can be accepted.
E-learning
http://mdg.vsb.cz/portal
Other requirements
There are no additional requirements for the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Integral calculus of functions of several independent variables. Two-dimensional integrals on coordinate rectangle, on bounded subset of R2.
2. Transformation two-dimensional integrals, geometrical and physical applications.
3. Three-dimensional integrals on coordinate cube, on bounded subset of R3.
4. Transformation of three-dimensional integrals, geometrical and physical applications.
5. Line integral of the first and of the second kind.
6. Independence line integral on path, Green´s theorem.
7. Applications of line integrals.
8. Series. Infinite number series. Definition, sum of a series, necessary convergence condition, harmonic series, geometric series.
9. Convergency tests, ratio test, Cauchy's root test, comparison test, integral test.
10. Alternating series - absolute and conditional convergency, Leibniz test.
11. Power series - convergency interval, radius of convergence, sum of a powerseries.
12. Taylor expansion, applications.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.