Course detail
Selected parts from mathematics I.
FEKT-BPC-VPAAcad. year: 2025/2026
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
Entry knowledge
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.
Rules for evaluation and completion of the course
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.
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.
Students completing this course should be able to:
- 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.
Study aids
Prerequisites and corequisites
Basic literature
Recommended reading
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-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-ZVUK , 0 year of study, winter semester, elective
specialization AUDB-TECH , 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 BPC-NCP Bachelor's 0 year of study, winter semester, elective
- Programme BPC-EMU Bachelor's 0 year of study, winter semester, elective
- Programme BIT Bachelor's 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
- Mapping theory, limit and continuity of functions of more variables
- Vector analysis
- Derivative of a composed mapping
- Local, constrained and absolute extrema, Lagrange method.
- Integral calculus of functions of more variables
- Calculation of n-dimensional integrals using successive integration
- Transformation of double integrals, applications
- Transformation of triple integrals, applications
- Improper integral of functions of more variables
- Line integral in a scalar field, applications
- Line integral in a vector field, applications
- Surface integral in a scalar field, applications
- Surface integral in a vector field, integral theorems
Fundamentals seminar
Teacher / Lecturer
Syllabus
- Computation of limits of functions of more variables
- Computation of characteristics of scalar and vector fields
- Computation of a derivative of a composed mapping
- Computation of local, constrained and absolute extrema, Lagrange method.
- Construction of integral of functions of more variables
- Computation of n-dimensional integrals using successive integration
- Transformation of double integrals, evaluations and applications
- Transformation of triple integrals, evaluations and applications
- Improper integral of functions of more variables, evaluations
- Line integral in a scalar field, evaluations and applications
- Line integral in a vector field, evaluations and applications
- Surface integral in a scalar field, evaluations and applications
- Surface integral in a vector field, integral theorems, applications
Computer-assisted exercise
Teacher / Lecturer
Syllabus
- Computation of limits of functions of more variables
- Computation of characteristics of scalar and vector fields
- Computation of a derivative of a composed mapping
- Computation of local, constrained and absolute extrema, Lagrange method.
- Construction of integral of functions of more variables
- Computation of n-dimensional integrals using successive integration
- Transformation of double integrals, evaluations and applications
- Transformation of triple integrals, evaluations and applications
- Improper integral of functions of more variables, evaluations
- Line integral in a scalar field, evaluations and applications
- Line integral in a vector field, evaluations and applications
- Surface integral in a scalar field, evaluations and applications
- Surface integral in a vector field, integral theorems, applications