Course detail

Selected parts from mathematics

FEKT-CVPMAcad. year: 2011/2012

Multiple integrals , transformation of multiple integrals . Vector analysis.
Line integral in the scalar-valued and vector-valued field. Surface integral in the scalar-valued and vector-valued field.
Selected methods of solving of systems of differential equations, exponential of a matrix.
Stability of solutions of differential equations,
criterions of stability.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Šmarda, CSc.

Department

Department of Mathematics (UMAT)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

The ability to solve multiple integrals, line and surface integrals, systems of differential equations including of a stability
and applications in electrical engineering.

Prerequisites

The subject knowledge on the secondary school level is required.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

Course curriculum

1) Characteristics of the scalar-valued and vector-valued fields.
2) Extrema of a function of several variables.
3) Double integral, transformation of the double integral.
4) Triple integral, transformation of the triple integral.
5) Improper multiple integral.
6) Line integral in the scalar-valued field.
7) Line integral in the vector-valued field.
8) Surface integral in the scalar-valued field.
9) Surface integral in the vector-valued field.
10) Integral theorems.
11) Qualitative properties of systems of differential equations.
12) Eliminative method.
13) Method of eigenvalues and eigenvectors.

Work placements

Not applicable.

Aims

Mastering basic notions and methods of calculations of multiple integrals, line and
surface integrals, solving of systems of differential equations including of investigations
of a stability of solutions of differential equations and applications of selected functions
with solving of dynamical systems.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ŠMARDA, Z., RUŽIČKOVÁ, I.: Vybrané partie z matematiky, el. texty na PC síti.

Recommended reading

BRABEC, J., HRUZA, B.: Matematická analýza II, SNTL/ALFA, Praha 1986, 579s.
GARNER, L.E.: Calculus and Analytical Geometry. Brigham Young University, Dellen publishing Company, San Francisco,1988, ISBN 0-02-340590-2. (EN)
KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123s.

Classification of course in study plans

  • Programme EECC Bc. Bachelor's

    branch BC-AMT , 2 year of study, summer semester, elective interdisciplinary
    branch BC-SEE , 2 year of study, summer semester, elective interdisciplinary
    branch BC-MET , 2 year of study, summer semester, elective interdisciplinary
    branch BC-EST , 2 year of study, summer semester, elective interdisciplinary
    branch BC-TLI , 2 year of study, summer semester, elective interdisciplinary

Type of course unit

 

Lecture

52 hod., optionally

Teacher / Lecturer

doc. RNDr. Zdeněk Šmarda, CSc.

Syllabus

1.Some notions from differential calculus of a function of multi variables.
2.Multiple integrals.
3.Transformation of multiple integrals.
4.Improper multiple integrals.
5.Lines in Rn, undirected line integral.
6.Directed line integral, indenpedence on an
integrable way.
7.Surfaces in R3, undirected surface integral.
8.Orientation of a surface, directed surface
integral.
9.Integral theorems.
10.Systems of differential equations, elementary
methods of solving.
11.General methods of solving of differential
equations.
12.Solving of systems of differential equations
with selected rightside,stability of solutions.
13.Criterions of stability of solutions.