Course detail
Selected Parts from Mathematics II
FEKT-BPA-VPMAcad. year: 2021/2022
The aim of this course is to introduce the basics of calculation of improper multiple integral and basics of solving of linear differential equations using delta function and weighted function.
In the field of improper multiple integral, main attention is paid to calculations of improper multiple integrals on unbounded regions and from unbounded functions.
In the field of linear differential equations, the following topics are covered: Eliminative solution method, method of eigenvalues and eigenvectors, method of variation of constants, method of undetermined coefficients, stability of solutions.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Offered to foreign students
Learning outcomes of the course unit
- calculate improper multiple integral on unbounded regions and from unbounded functions.
- apply a weighted function and a delta function to solving of linear differential equations.
- select an optimal solution method for given differential equation.
- investigate a stability of solutions of systems of differential equations.
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 improper multiple integral (10 points), three from application of a weighted function and a delta function (3 X 10 points) and three from analytical solution method of differential equations (3 x 10 points)).
Course curriculum
2) Improper multiple integral
3) Impulse function and delta function, basic properties
4) Derivative and integral of the delata function
5) Unit function and its relation with the delta function, weighted function
6) Solving differential equations of the n-th order using weighted functions
7) Relation between Dirac function and weighted function
8) Systems of differential equations and their properies
9) Eliminative solution method
10) Method of eigenvalues and eigenvectors
11) Method of variation of constants and method of undetermined coefficients
12) Differential transformation solution method of ordinary differential equations
13) Differential transformation solution method of functional differential equations
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
Classification of course in study plans