Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |

Subject guarantor | doc. RNDr. Jarmila Doležalová, CSc. | Subject version guarantor | Mgr. Arnošt Žídek, Ph.D. |

Study level | undergraduate or graduate | ||

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | 2019/2020 |

Intended for the faculties | FS | Intended for study types | Follow-up Master |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

DOL30 | doc. RNDr. Jarmila Doležalová, CSc. | ||

LUN44 | Mgr. Milena Luňáčková, Ph.D. | ||

VAV14 | RNDr. Eva Vavříková, Ph.D. | ||

ZID76 | Mgr. Arnošt Žídek, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+3 |

Part-time | Credit and Examination | 16+4 |

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.

Lectures

Individual consultations

Tutorials

Other activities

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.

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992.
ISBN 0-201-1805456

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992.
ISBN 0-201-1805456
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993.
ISBN 0-201-56519-6

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. (60 points is a maximum, but at least 20 points are necessary)
Classifications
Points obtained ECTS Grade
100-91 A
90-81 B
80-71 C
70-61 D
60-51 E
50-0 F
Points obtained National grading scheme
100-86 1 (excellent)
85-66 2 (very good)
65-51 3 (good)
50-0 4 (failed)
Topics for the theoretical part of the exam
Systems of n ordinary linear differential equations of the first order for n functions: definition, matrix representation
Elimination method for the systems of LDE
Euler method for the homogeneous systems of LDE
Two-dimensional integral on a rectangle
Two-dimensional integral on a bounded subset of R2
Transformation - polar coordinates
Geometrical and physical applications of the two-dimensional integral
Three-dimensional integrals on a cube, on a bounded subset of R3
Transformation - cylindrical and spherical coordinates,
Geometrical and physical applications of the three-dimensional integral
Scalar field, gradient
Vector field, divergence, rotation (curl)
Line integral of the first and of the second kind
Green´s theorem
Path independence for the line integral, potential
Geometrical and physical applications of the line integral
Infinite number series
Necessary condition for convergence
Geometric series
Harmonic series, generalized harmonic series, Leibniz series
Infinite series of functions, power series

http://www.studopory.vsb.cz
http://mdg.vsb.cz

No more requirements are put on the student.

Subject has no prerequisities.

Subject has no co-requisities.

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 completion are defined only for particular subject version and form of study

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