Czech

4

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Institute of Mathematics and Descriptive Geometry (MAT)

The ability to orientate in the basic notions and problems
of discrete and difference equations.
Solving problems in the areas cited in the annotation.

The subject knowledge in mathematics on the Bachelor´s and Magister´s degree level is requested.

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1. Basic notions and methods of investigation of discrete equations.
2. Discrete calculus (some difference relations based on corresponding continuous relations).
3. Difference equations and systems.
4. Basic notions used in difference equations.
5. Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points.
6. Stability of solution, repelling and attracting points and their illustration on examples.
7. Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients.
8. The method of variation of parameters.
9. The method of variation of constants.
10. Rovnice průhybu nosníku, řešení metodou diskrétních rovnic. Okrajové a počáteční podmínky.
11. Průhyb nosníku, řešení metodou diskrétních rovnic.
12.–13. Difference equations modelled with the aid of sampling.

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Discrete and difference equations are the mathematical base of many fields of engineering science. The purpose of this course is to develop the basic notions concerning the properties of solutions of such equations and to give methods of their applications.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

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39 hours, optionally

1. Basic notions and methods of investigation of discrete equations. 2. Discrete calculus (some difference relations based on corresponding continuous relations). 3. Difference equations and systems. 4. Basic notions used in difference equations. 5. Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points. 6. Stability of solution, repelling and attracting points and their illustration on examples. 7. Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients. 8. The method of variation of parameters. 9. The method of variation of constants. 10. Rovnice průhybu nosníku, řešení metodou diskrétních rovnic. Okrajové a počáteční podmínky. 11. Průhyb nosníku, řešení metodou diskrétních rovnic. 12.–13. Difference equations modelled with the aid of sampling.