Course detail

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.

90 % face-to-face, 10 % distance learning

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

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

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

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

Czech

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