Selected Parts from Mathematics 2
IVP2 FEEC BUT BPC-VPM Acad. year 2019/2020 Summer semester 5 credits
In the field of multiple integrals, the main attention is paid to calculations of multiple integrals on elementary regions and utilization of polar, cylindrical and spherical coordinates, calculations of a potential of vector-valued field and application of integral theorems.
Language of instruction
Subject specific learning outcomes and competences
- calculate local, constrained and absolute extrema of functions of several variables.
- calculate multiple integrals on elementary regions.
- transform integrals into polar, cylindrical and spherical coordinates.
- calculate line and surface integrals in scalar-valued and vector-valued fields.
- apply integral theorems in the field theory.
Mastering basic calculations of multiple integrals, especially transformations of multiple integrals and calculations of line and surface integrals in scalar-valued and vector-valued fields.
of stability of solutions of differential equations and applications of selected functions
with solving of dynamical systems.
Why is the course taught
Prerequisite kwnowledge and skills
- ŠMARDA, Z., RUŽIČKOVÁ, I.: Selected parts from Mathematics, el. version on UMAT server.
- KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123 p. (in Czech)
- BRABEC, J., HRUZA, B.: Matematická analýza II, SNTL/ALFA, Praha 1986, 579 p. (in Czech)
- GARNER, L.E.: Calculus and Analytical Geometry. Brigham Young University, Dellen publishing Company, San Francisco,1988, ISBN 0-02-340590-2.
Syllabus of lectures
- Differential calculus of functions of several variables, limit, continuity, derivative
- Vector analysis
- Local extrema
- Constrained and absolute extrema
- Multiple integral
- Transformation of multiple integrals
- Applications of multiple integrals
- Line integral in a scalar-valued field
- Line integral in a vector-valued field
- Potential, Green's theorem
- Surface integral in a scalar-valued field
- Surface integral in a vector-valued field
- Integral theorems
The written examination is evaluated by a maximum of 70 points. It consists of seven tasks (one from extrema of functions of several variables (10 points), two from multiple integrals (2 X 10 points), two from line integrals (2 x 10 points) and two from surface integrals (2 x 10 points)).
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.
Course inclusion in study plans