Course detail

Mathematical Analysis 2

FEKT-SMA2Acad. year: 2005/2006

Linear differential equations - basic notions, methods of solution. Linear differential equations of higher order with constant coefficients. Use of Laplace transforms to solve differential equations. Number series in real and complex domains, convergence criteria. Power series. Taylor's expansion.
Trigonometric Fourier's series. Functions of several variables, limit, continuity. Partial and directional derivatives, differentials, gradient. Derivatives of higher order, Taylor formula. Derivatives of composite functions, implicitly defined functions. Extrema of functions of several variables. Conditional extrema.

Language of instruction

Czech

Number of ECTS credits

8

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Diblík, DrSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

Solving problems in the areas cited in the annotation above
by using basic rules and knowledges. Solving these problems by using modern mathematical software.

Prerequisites

It is a course of the non-structured ending study program

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Explanation of the notion of differential equation. Solving of simplest classes of differentiale quations (including, except others, Laplace transform). Notion of functions of several variables. Using of tool of functions of several variables,
their extrema. The practical aspects of applications of these methods and their use in solving concrete problems (including the application of contemporary mathematical software in the laboratories) are emphasized.

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

Not applicable.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Angot, A.:Užitá matematika pro elektrotechnické inženýry,SNTL, SVTL, 1972.
Brabec, J., Hrůza, B.:Matematika II,SNTL/ALFA, 1986.
Nagy, J. , Nováková, E., Vacek M.:Integrální počet,SNTL, 1984, MVŠT, sešit VI.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EI-B3 Bachelor's

    branch B3-KAM , 1. year of study, summer semester, compulsory
    branch B3-EST , 1. year of study, summer semester, compulsory
    branch B3-SEE , 1. year of study, summer semester, compulsory
    branch B3-EVM , 1. year of study, summer semester, compulsory

  • Programme EI-M5 Master's

    branch M5-KAM , 1. year of study, summer semester, compulsory

  • Programme EI-M5 Master's

    branch M5-KAM , 1. year of study, summer semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EST , 1. year of study, summer semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EST , 1. year of study, summer semester, compulsory

  • Programme EI-M5 Master's

    branch M5-SEE , 1. year of study, summer semester, compulsory

  • Programme EI-M5 Master's

    branch M5-SEE , 1. year of study, summer semester, compulsory
    branch M5-EVM , 1. year of study, summer semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EVM , 1. year of study, summer semester, compulsory

Type of course unit

 

Lecture

39 hours, compulsory

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

Syllabus

Linear differential equations - basic notions, methods of solution.
Linear differential equations of higher order with constant coefficients.
Use of Laplace transforms to solve differential equations.
Number series in real and complex domains, convergence criteria.
Power series.
Taylor's expansion.
Trigonometric Fourier's series.
Functions of several variables, limit, continuity.
Partial and directional derivatives, differentials, gradient.
Derivatives of higher order, Taylor formula.
Derivatives of composite functions, implicitly defined functions.
Extrema of functions of several variables.
Conditional extrema.

Fundamentals seminar

48 hours, compulsory

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

Syllabus

Linear differential equations - basic notions, methods of solution.
Linear differential equations of higher order with constant coefficients.
Use of Laplace transforms to solve differential equations.
Number series in real and complex domains, convergence criteria.
Power series.
Taylor's expansion.
Trigonometric Fourier's series.
Functions of several variables, limit, continuity.
Partial and directional derivatives, differentials, gradient.
Derivatives of higher order, Taylor formula.
Derivatives of composite functions, implicitly defined functions.
Extrema of functions of several variables.
Conditional extrema.

Laboratory exercise

4 hours, compulsory

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

Syllabus

Differential equations.
Series.
Functions of several variables.