Czech

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Institute of Mathematics and Descriptive Geometry (MAT)

The students manage the subject to the level of understanding foundation of the modern methods of ordinary and partial differential equations in the engineering applications.

Basics of the theory of one- and more-functions. Differentiation and intgration of functions.

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Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1. Basics of ordinary differential equations focussing on engineering applications – classic solution, Cauchy problem and boundary problems (classes).
2. Analytical methods used to solve boundary problems in ordinary secod and fourth order differential equations.
3. Methods of solution of non-homogeneous boundary problems – Fourier method,
4. Green´s function, variation of constants method.
5. Solutions of non-linear differential equations with given boundary conditions.
6. Sobolev spaces and generalized solutions and reason for using such notions.
7. Variational methods of solutions.
8. Introduction to the theory of partial differential equations of two variables – classes and basic notions.
9. Classic solution of a boundary problem (classes), properties of solutions.
10. Laplace and Fourier transform – basic properties.
11. Fourier method used to solve evolution equations, difussion problems, wave equation.
12. Laplace method used to solve evolution equations - heat transfer equation.
13. Equations used in the theory of elasticity.

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Understanding the notion of generalized solutions to ordinary differential equations. Getting acquainted with principles of the modern methods used to solve odrinary and partial differential equations in transport structures.

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

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BARTÁK, J., HERRMANN, L., LOVICAR, V., VEJVODA, O.: Partial Differential Equations. Ellis Horwood and SNTL, 1991. (EN)
FARLOW, S. J.: Partial Differential Equations. John Wiley&Sons, 1982. (EN)
MÍKA, S., KUFNER, A.: Okrajové úlohy pro obyčejné diferenciální rovnice.. SNTL, 1983. (CS)

Not applicable.