714-0016/01 – Mathematics (M)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | Mgr. Jakub Stryja, Ph.D. | Subject version guarantor | Mgr. Jakub Stryja, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2014/2015 | Year of cancellation | 2019/2020 |
| 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
Lectures
Individual consultations
Tutorials
Project work
Summary
Double and triple integrals and their applications. Line integral and its
applications. Infinite series, power series.
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
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 Integral calculus of functions of several independent variables. Two-dimensional integrals on coordinate rectangle, on bounded subset of R2.
2 Transformation two-dimensional integrals.
3 Geometrical and physical applications.
4 Three-dimensional integrals on coordinate cube, on bounded subset of R3. transformation of three-dimensional integrals.
5 Geometrical and physical applications.
6 Line integral of the first and of the second kind.
7 Independence line integral on path, Green´s theorem.
8 Applications.
9 Series. Infinite number series. Definition, sum of a series, necessary convergence condition, harmonic series, geometric series.
10 Convergency tests, ratio test, Cauchy's root test, comparison test, integral test.
11 Alternating series - absolute and conditional convergency, Lebniz test.
12 Power series - convergency interval, radius of convergence, sum of a powerseries.
13 Taylor expansion, applications.
14 Reserve.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction