Selected Parts from Mathematics 1
IVP1 FEEC BUT BVPA Acad. year 2017/2018 Summer semester 5 credits
Language of instruction
Subject specific learning outcomes and competences
- Calculate local, constrained and absolute extrema of functions of several variables.
- calculate multiple integrals o, elementary regions,
- transform integrals into polar, cylindrical and sferical coordinates,
- calculate line and surface integrals in scalar-valued and vector-valued fields,
- apply integral theorems in the field theory.
Prerequisite kwnowledge and skills
- ŠMARDA, Z., RUŽIČKOVÁ, I.: Vybrané partie z matematiky, el. texty na PC síti.
- KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123 p.
- BRABEC, J., HRUZA, B.: Matematická analýza II, SNTL/ALFA, Praha 1986, 579 p.
- 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.
Written examination is evaluated by maximum 70 points. It consist 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