Selected Parts from Mathematics 1
IVP1 FEEC BUT BPC-VPA Acad. year 2019/2020 Winter semester 5 credits
In the field of improper multiple integral, the 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, a method of eigenvalues and eigenvectors, method of variation of constants, a method of undetermined coefficients, the stability of solutions.
Language of instruction
Subject specific learning outcomes and competences
- 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 the given differential equation.
- investigate the stability of solutions of systems of differential equations.
Why is the course taught
Prerequisite kwnowledge and skills
- ŠMARDA, Z., RUŽIČKOVÁ, I.: Vybrané partie z matematiky, el. texty na PC síti. (CS)
- KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123s. (CS)
- BRABEC, J., HRUZA, B.: Matematická analýza II,SNTL/ALFA, Praha 1986, 579s. (CS)
- GARNER, L.E.: Calculus and Analytical Geometry. Brigham Young University, Dellen publishing Company, San Francisco,1988, ISBN 0-02-340590-2.
Syllabus of lectures
- Basic properties of multiple integrals.
- Improper multiple integral
- Impulse function and delta function, basic properties
- Derivative and integral of the delata function
- Unit function and its relation with the delta function, the weighted function
- Solving differential equations of the n-th order using weighted functions
- The relation between Dirac function and weighted function
- Systems of differential equations and their properties
- Eliminative solution method
- Method of eigenvalues and eigenvectors
- Method of variation of constants and method of undetermined coefficients
- Differential transformation solution method of ordinary differential equations
- Differential transformation solution method of functional differential equations
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)).
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.
Course inclusion in study plans