Course detail

Differential equations in electrical engineering

FEKT-SDREAcad. year: 2005/2006

1.Ordinary differential equations of the first order. (Basic notions. Existence and unicity of solutions. Basic classes of equations). 2. Ordinary differentiál equations of the n-th order. Qualitative theory. Linear equations od n-th order.
3. Systems of ordinary differential equations. Linear homogeneous and nonhomogeneous systems. Systems with constant coefficients. The vector form of solution. 4. Apllication of differential equations. Linear systems with noncontinuous coefficients. Mechanical systems. Van der Pool equations.
5. Partial differential equations. Classes of equations, canonical forms. Partial differential equations of the first order. Some methods of solution of second order partial differential equations.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Diblík, DrSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The ability to orientate in the basic notions and problems
of differential equations.
Solving problems in the areas cited in the annotation above
by use of these methods. 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

Practical skills and ability to solve certain classes of differential equations as well the ability to use theoretical apparat for it will be positively estimated.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Differential equations are the base of many fields of engineering science. The purpose of this course is to develop the basic notion concerning the properties of solutions of differential equations and to give the basic technique for solution of differential equations. In this course not only several exact solution methods are explained, but attention is focused also on possibilities of getting information concerning properties of solutions. Methods are illustrated on concrete electroengineering examples.

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

Greguš, M., Švec, M., Šeda, V.:Obyčajné diferenciálne rovnice,ALFA, Bratislava, 1995
Angot, A.,:Užité matematika pro elektrotechnické inženýry,SNTL, SVTL, 1972
Kalas, J., Ráb, M.:Obyčejné diferenciální rovnice,Masarykova universita, Brno, 2001
Kuben Jaromír, Obyčejné diferenciální rovnice, VA, Brno, 2000
M. Ráb: Metody řešení obyčejných diferenciálních rovnic. MU Brno, 1998, ISBN 80-210-1818-6

Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

Syllabus

Ordinary differential equations of the first order.
Basic notions. Existence and unicity of solutions. Basic classes of equations.
Ordinary differentiál equations of the n-th order. Qualitative theory.
Linear equations od n-th order.
Systems of ordinary differential equations.
Linear homogeneous and nonhomogeneous systems.
Systems with constant coefficients.
The vector form of solution. Application of differential equations.
Linear systems with noncontinuous coefficients.
Mechanical systems. Van der Pool equations.
Partial differential equations. Classes of equations, canonical forms.
Partial differential equations of the first order.
Some methods of solution of second order partial differential equations.

Fundamentals seminar

26 hours, optionally

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

Syllabus

VUT

Faculties

University Institutes

Parts

Differential equations in electrical engineering

Type of course unit