Course detail
Selected parts from mathematics I.
FEKT-BPC-VPAAcad. year: 2021/2022
The aim of this course is to introduce the basics of calculation of local, constrained and absolute extrema of functions of several variables, double and triple inegrals, line and surface integrals in a scalar-valued field and a vector-valued field including their physical applications.
In the field of multiple integrals , main attention is paid to calculations of multiple integrals on elementary regions and utilization of polar, cylindrical and sferical coordinates, calculalations of a potential of vector-valued field and application of integral theorems.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
- calculate local, constrained and absolute extrema of functions of several variables.
- calculate multiple integrals on 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.
Prerequisites
From the BMA1 and BMA2 courses, the basic knowledge of differential and integral calculus and solution methods of linear differential equations with constant coefficients is demanded. Especially, the student should be able to calculate derivative (including partial derivatives) and integral of elementary functions.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
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)).
Course curriculum
2) Vector analysis
3) Local extrema
4) Constrained and absolute extrema
5) Multiple integral
6) Transformation of multiple integrals
7) Applications of multiple integrals
8) Line integral in a scalar-valued field.
9) Line integral in a vector-valued field.
10) Potential, Green's theorem
11) Surface integral in a scalar-valued field.
12) Surface integral in a vector-valued field.
13) Integral theorems.
Work placements
Aims
Mastering basic calculations of multiple integrals, especialy tranformations of multiple integrals and calculations of line and surface integrals in scalar-valued and vector-valued fields.
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
Elearning
Classification of course in study plans
- Programme BKC-EKT Bachelor's 0 year of study, winter semester, elective
- Programme BKC-MET Bachelor's 0 year of study, winter semester, elective
- Programme BKC-SEE Bachelor's 0 year of study, winter semester, elective
- Programme BKC-TLI Bachelor's 0 year of study, winter semester, elective
- Programme BPC-AMT Bachelor's 0 year of study, winter semester, elective
- Programme BPC-AUD Bachelor's
specialization AUDB-TECH , 0 year of study, winter semester, elective
specialization AUDB-ZVUK , 0 year of study, winter semester, elective - Programme BPC-ECT Bachelor's 0 year of study, winter semester, elective
- Programme BPC-IBE Bachelor's 0 year of study, winter semester, elective
- Programme BPC-MET Bachelor's 0 year of study, winter semester, elective
- Programme BPC-SEE Bachelor's 0 year of study, winter semester, elective
- Programme BPC-TLI Bachelor's 0 year of study, winter semester, elective
- Programme IT-BC-3 Bachelor's
branch BIT , 2 year of study, winter semester, elective
- Programme BIT Bachelor's 2 year of study, winter semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2) Vektorová analýza
3) Lokální extrémy funkce více proměnných
4) Vázané a absolutní extrémy
5) Vícerozměrný integrál.
6) Transformace vícerozměrných integrálů
7) Aplikace vícerozměrných integrálů
8) Křivkový integrál ve skalární poli
9) Křivkový integrál ve vektorovém poli
10) Potenciál , Greenova věta
11) Plošný integrál ve skalárním poli
12) Plošný integrál ve vektorovém poli
13) Integrální věty
Elearning