Course detail
Selected Parts from Mathematics for Engineers
FEKT-MPC-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
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
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 MPC-KAM Master's 1 year of study, winter semester, compulsory
Type of course unit
Elearning