Czech

Not applicable.

Solution of algebraic equations and system of linear equations, differential and integral calculus of functions of one and more variables, ordinary differential equations.

The examination consists of a practical and a theoretical part.
Practical part: solving examples of P.D.E.:
1) solution of the 1st order equation,
2) classification and transformation of the 2nd order equation to its canonical form,
3) formulation of an initial boundary value problem related to the physical setting
and finding its solution by means of the Fourier series method.
Theoretical part: 3 questions from the theory of P.D.E.
Absence has to be made up by self-study using lecture notes.

The aim of the subject is to provide students with the basic knowledge
of the partial differential equations, particularly equations of
mathematical physics, their basic properties, methods of solving them
and their application in mathematical modelling. Another goal is to teach
the students to formulate and solve the basic problems of mathematical physics.
Elements of the theory of P.D.E. and survey of their application in mathematical modelling. Ability to formulate mathematical model of the selected problems of mathematical physics and to compute the solution in some simple cases.

Not applicable.

Not applicable.

Arsenin, V. J.: Metody matematičeskoj fyziky i specialnyje funkcii, Nauka, Moskva 1974, překlad do slovenštiny: Matematická fyzika. Základné rovnice a špeciálne funkcie. Alfa, Bratislava, 1977. (RU)
Evans, L. C.: Partial differential equations, American Math. Society Providence 1998. (EN)
Sobolev, S. L.: Partial differential equations of mathematical physics Pergamon Press, Oxford 1964 (EN)
T. A. Bick: Elementary boundary value problems. Marcel Dekker, New York 1993 (EN)
Williams, W. E.: Partial Differential Equations, Clarendon Press, Oxford 1980. (EN)

Drábek, P., Holubová, G.: Elements of Partial Differential Equations, De Gruyter, Berlin, 2014 (EN)
J. Franců: Parciální diferenciální rovnice. Akad. nakl. CERM, Brno 2011 (CS)
Renardy, M., Rogers, R., C.: An introduction to partial differential equations, Springer, New York 2004. (EN)
V. J. Arsenin: Matematická fyzika, Alfa, Bratislava 1977 (SK)