Course detail

The multiple integral and differential equations.

FEKT-SIDRAcad. year: 2005/2006

Construction and calculation of the integral in several variables, transformation of integrals, applications. Orientation a curve,construction and calculation the line integral of scalar-valued and vector-valued fields. Orientation of a surface,construction and calculation of surface integrals of scalar-valued and vector-valued fields, Integral's Theorems. Basic notions of the theory of linear differential equations with constant coefficients,
numerical method of solutions of differential equations.

Language of instruction

Czech

Number of ECTS credits

7

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 ,systems of differential
equations and basic applications in electrical engineering.

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

Mastering basic notions of the integral in several variables
and elementary methods solution of system linear differential
equations with constant coefficients.

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

D.B.Small, J.M.Hosack:Calculus an integrated approach,Mc Graw-Hill Publishing Company, 1990
J.Brabec, B.Hrůza:Matematika II,SNTL/ALFA, 1986
J.Škrášek:Základy aplikované matematiky II,SNTL, 1976

Recommended reading

GARNER,L.E: Calculus and Analytic Geometry. Dellen Publishing Company, Francisco 1988, ISBN 0-02-340590-2.

Classification of course in study plans

  • Programme EI-B3 Bachelor's

    branch B3-KAM , 2. year of study, winter semester, compulsory
    branch B3-EST , 2. year of study, winter semester, compulsory
    branch B3-SEE , 2. year of study, winter semester, compulsory
    branch B3-EVM , 2. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-KAM , 2. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-KAM , 2. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EST , 2. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EST , 2. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-SEE , 2. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-SEE , 2. year of study, winter semester, compulsory
    branch M5-EVM , 2. year of study, winter semester, compulsory

  • Programme EI-M5 Master's

    branch M5-EVM , 2. year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hours, compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Šmarda, CSc.

Syllabus

The integral in several variables, calculation.
Transformation of the integral, applications.
Curves, line integral of a scalar-valued function.
Vector-valued fields, line integral of a vector-valued field.
The surface integral of a scalar-valued function.
The surface integral of a vector-valued field, rotation, divergence.
Integral's Theorems of the vector analysis.
Basic notions of ordinary differential equations.
Theory of linear differential equations of n-th order.
Analytical methods of solutions of ordinary differential equations.
Systems of linear differential equations.
Systems with constant coefficients.
Numerical methods of solutions of differential equations.

Fundamentals seminar

39 hours, compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Šmarda, CSc.

Syllabus

Multiple integrals, transformation of integrals, applica- tions.
Scalar-valued and vector-valued field, the line and surfa- ce integral, Integral's Theorems.
Linear differential equations of n-th order.
Systems of linear differential eqauations.
Numerical methods of solutions of differential equations.