Course detail
Selected parts from mathematics II.
FEKT-XPC-VPMAcad. year: 2020/2021
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
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) Derivative and integral of the delata function
3) Solving differential equations of the n-th order using weighted functions
4) Systems of differential equations and their properties
5) Eliminative solution method
6) Method of eigenvalues and eigenvectors
7) Method of variation of constants and method of undetermined coefficients
8) Differential transformation solution method of ordinary differential equations
9) Differential transformation solution method of functional differential equations
10) Diference operator, summation, classification od difference equations
11) Shift operator, solution methods of difference equations with variable coefficients
12) Solution methods of linear difference equations with constant coefficients
13) Solution methods of systems of difference 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
KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123s. (CS)
Elearning
Classification of course in study plans
- Programme BPC-AMT Bachelor's 0 year of study, summer semester, elective
- Programme BPC-AUD Bachelor's
specialization AUDB-TECH , 0 year of study, summer semester, elective
specialization AUDB-ZVUK , 0 year of study, summer semester, elective - Programme BPC-ECT Bachelor's 0 year of study, summer semester, elective
- Programme BPC-IBE Bachelor's 0 year of study, summer semester, elective
- Programme BPC-MET Bachelor's 0 year of study, summer semester, elective
- Programme BPC-SEE Bachelor's 0 year of study, summer semester, elective
- Programme BPC-TLI Bachelor's 0 year of study, summer semester, elective
- Programme BKC-EKT Bachelor's 0 year of study, summer semester, elective
- Programme BKC-MET Bachelor's 0 year of study, summer semester, elective
- Programme BKC-SEE Bachelor's 0 year of study, summer semester, elective
- Programme BKC-TLI Bachelor's 0 year of study, summer semester, elective
- Programme IT-BC-3 Bachelor's
branch BIT , 2 year of study, summer semester, elective
- Programme BIT Bachelor's 2 year of study, summer semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2) Nevlastní vícerozměrný integrál
3) Impulzní funkce a delta funkce, základní vlastnosti.
4) Derivace a integrál delta funkce
5) Jednotková funkce a její vztah s delta funkcí, váhová funkce.
6) Řešení diferenciálních rovnic n-tého řádu užitím váhových funkcí
7) Vztah Diracovy funkce a váhové funkce
8) Systémy diferenciálních rovnice a jejich vlastnosti.
9) Eliminační metoda řešení.
10) Metoda vlastních čísel a vlastních vektorů.
11) Variace konstant a metoda neurčitých koeficientů
12) Diferenciální transformační metoda pro obyčejné diferenciální rovnice
13) Diferenciální transformační metoda pro diferenciální rovnice se zpožděným argumentem
Elearning