Czech

5

Not applicable.

The student should be able to apply the basic knowledge of analytic geometry and mathamatical analysis on the secondary school level: to explain the notions of general, parametric equations of lines and surfaces and elementary functions.
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.

The student's work during the semestr (written tests and homework) is assessed by maximum 30 points.
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.

The aim of this course is to introduce the basics of improper multiple integrals, systems of differential equations including of investigations 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 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.

Not applicable.

Not applicable.

HLAVIČKOVÁ, I. KOLÁŘOVÁ, E., ŠMARDA,Z., Vybrané partie z matematiky II. -učební text (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)

14 hours, compulsory

1. Impulse functions,  solving differential  equations using a weight function
2. Systems  of  differential  equations,  Elimination  method
3. Constants variation  method ,  Method  of eigenvalue numbers  and eigenvalue vectors
4. Method of undetermined coefficients
5. Differential  transform method (DTM) 
6.  DTM  for systems of differential  equations, delayed systems
7. Difference equations, rules for differences, summation
8. Solving linear homogeneous and non-homogeneous difference equations
9. Gamma function,  solving specific nonlinear  difference equations 
10. Solving systems of difference equations
11. Fractional  calculus,  Mittag-Leffler  functions
12. Solving fractional differential  equations in the sense of  Caputo  a Riemann-Liouville  derivative
13. Solving fractional systems of differential  equations,  impulse  characterizations