Course detail
Selected parts from mathematics
FEKT-BVPMAcad. year: 2012/2013
Extrema of a function of several variables.
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
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
and applications in electrical engineering
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
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
Aims
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
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading
GARNER, L.E.: Calculus and Analytical Geometry. Brigham Young University, Dellen publishing Company, San Francisco,1988, ISBN 0-02-340590-2.
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 B-MET , 3 year of study, winter semester, elective interdisciplinary
branch B-TLI , 3 year of study, winter semester, elective interdisciplinary
branch B-AMT , 3 year of study, winter semester, elective interdisciplinary
branch B-SEE , 3 year of study, winter semester, elective interdisciplinary
branch B-EST , 3 year of study, winter semester, elective interdisciplinary - Programme EEKR-CZV lifelong learning
branch EE-FLE , 1 year of study, winter semester, elective interdisciplinary
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.