310-3141/03 – Mathematics IV (MIV)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FS | 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
Other activities
Summary
Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions, Euler method for homogeneous systems of n equations for n functions. Integral calculus of functions of several independent variables: two-dimensional integrals, three-dimensional integrals, vector analysis, line integral of the first and the second kind, surface integral of the first and second kind. Infinite series: number series, series of functions, power series.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Seminar
Attending the seminar is required, only 20 % of missed lessons will be excused. It is also necessary to elaborate the home project in a form specified by the lecturer and a student is awarded 5 points for the project. Several tests will be carried out during the semester, a student can acquire up to 15 points.
Examination
The exam consists of two parts:
I) Practical part - tests the ability of solving practical problems. (60 points is a maximum, but at least 20 points are necessary)
II) Theoretical part - examines the understanding of the underlying theoretical concepts. (20 points is a maximum, but at least 5 points are necessary)
E-learning
http://www.studopory.vsb.cz (in Czech language)
http://lms.vsb.cz
Other requirements
No more requirements are put on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Syllabus of lecture
1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions
2 Euler method for homogeneous systems of n equations for n functions
3 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2
4 Transformation - polar coordinates, geometrical and physical applications
5 Three-dimensional integrals on coordinate cube, on bounded subset of R3
6 Transformation - cylindrical and spherical coordinates, geometrical and physical applications
7 Vector analysis, gradient
8 Divergence, rotation
9 Line integral of the first and of the second kind
10 Green´s theorem, potential
11 Geometrical and physical applications
12 Infinite number series
13 Infinite series of functions, power series
Syllabus of seminar
1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions
2 Euler method for homogeneous systems of n equations for n functions
3 Euler method for homogeneous systems of n equations for n functions, test
4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2
5 Transformation - polar coordinates
6 Geometrical and physical applications
7 Three-dimensional integrals on coordinate cube, on bounded subset of R3
8 Transformation - cylindrical and spherical coordinates
9 Geometrical and physical applications, test
10 Vector analysis, gradient
11 Divergence, rotation
12 Line integral of the first kind
13 Line integral of the second kind, test
14 Geometrical and physical applications
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks