Partial differential equations

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Department of Technical Mathematics

Synopsis:

The aim of the course: Introduction in methods of the classical and the modern theory of the partial differential equations

Formulation of the underlying boundary value problems and initial boundary value problems for the partial differential equations of the elliptic, parabolic and hyperbolic types in the frame of the classical theory of the PDEs.

The theory is illustrated on the Laplace equation, the Poisson equation, the heat equation, and the wave equation.

The properties of these equations and their solutions are explained.

Modern theory is explained on the example of the 2nd order differential equations of the elliptic type and on the systems of PDEs very often used in mathematical models in fluid dynamics.

Requirements:

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Study materials:

Evans, L.C.: Partial Differential Equations. American Mathematical Society, series „Graduate Studies in Mathematics,“ Vol. 19, New York 1997.

Drábek, Pavel, and Gabriela Holubová. Elements of Partial Differential Equations, De Gruyter, Inc., 2014.

Recommended literature: Following the individual needs of students

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: