Course detail

Selected parts from mathematics

FEKT-BVPAAcad. year: 2012/2013

Impulse funcdtions, delta function-
Derivative and integral of the delata function
Weighted functions and their applications for solving of differential equations of the n-th order
Systems of linear differential equations
Analytic solution methods
Vector analysis, multiple integrals
Applications of multiple integrals
Improper multiple integral

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Šmarda, CSc.

Department

Department of Mathematics (UMAT)

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) Impulse function and delta function, basic properties
2) Derivative and integral of the delata function
3) Unit function and its relation with the delta function, weighted function
4) Solving of differential equations of the n-th order using weighted functions
5) Systems of differential equations
6) Eliminative solution method
7) Method of eigenvalues and eigenvectors
8) Method of variation of constants and method of undetermined coefficients
9) Characteristics of scalar and vector fields
10) Multiple integral
11) Transformation of multiple integrals
12) Applications of multiple integrals
13 ) Improper multiple integral

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

KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123s.
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.

Classification of course in study plans

  • Programme EEKR-B Bachelor's

    branch B-AMT , 2. year of study, summer semester, optional specialized
    branch B-EST , 2. year of study, summer semester, optional interdisciplinary
    branch B-MET , 2. year of study, summer semester, optional interdisciplinary
    branch B-SEE , 2. year of study, summer semester, optional interdisciplinary
    branch B-TLI , 2. year of study, summer semester, optional interdisciplinary

  • Programme EEKR-CZV lifelong learning

    branch ET-CZV , 1. year of study, summer semester, optional interdisciplinary

Type of course unit

 

Lecture

39 hours, 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.

The other activities

13 hours, compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Šmarda, CSc.